Polarization-sensitive spectral interferometry

ABSTRACT

A polarization sensitive spectral interferometer apparatus and method for analyzing a sample by optical energy reflected from the sample. The polarization sensitive spectral interferometer apparatus and method determines polarization properties of the sample by optical energy reflected from the sample.

CROSS-RELATED APPLICATIONS

The present application is a divisional application from U.S.application Ser. No. 12/131,825, filed Jun. 2, 2008, which claimspriority to U.S. Provisional Application Ser. No. 60/932,546, filed May31, 2007, and claims priority to U.S. patent application Ser. No.11/446,683, filed Jun. 5, 2006, which issued as U.S. Pat. No. 7,782,224on Aug. 24, 2010, as a continuation-in-part, all incorporated byreference herein.

BACKGROUND OF THE INVENTION

The field of the invention generally relates to optical imaging, andmore specifically relates to Optical Coherence Tomography (“OCT”)systems and methods.

Spectral modifications resulting from interference of light in, alsoknown as channeled spectra can be observed with various spectralinterferometric techniques, commonly consisting of a nonscanninginterferometer and spectrometer in the detection path in OCT systems.The superposition of two light beams that are identical except for arelative optical path-length difference L results in a new spectra withripples that have minima at wavelength λ whenever (n+½)λ=L. If theoptical path length difference is constant over the bandwidth of light,the spacing between the adjacent minima of the resultant spectrum in theoptical frequency (v) domain is a constant c/L, where c is the speed oflight.

The interference fringes in the spectral domain can be obtained byperforming Fourier transform of those recorded in the time domain,distinct differences are recognized between these two measurements. Whenthe optical path length difference between two interfering beams, L=c τ,of the source light is much greater than the source temporal coherencelength, high visibility interference fringes are not observed in thetime domain. In the spectral domain, however, high visibility fringesare formed irrespective of how long or short the optical path-lengthdifference may be. Additionally, superior sensitivity and signal tonoise ratio of spectral interferometry over time-domain approaches arerecognized.

Channeled spectra recorded by spectral interferometers have been used tomeasure absolute distance, dispersion, and both absolute distance anddispersion. By analogy with a two-beam interferometer, the two axes ofan optically anisotropic sample or optical fiber can be regarded as twobeam paths, while a polarizer placed at the exit end of a sample undertest or optical fiber can superpose light from the two beam paths togenerate interference fringes in the spectral domain. In practice,polarization control is difficult to realize, since thepolarization-mode dispersion in fiber is random and the polarizationtransformations introduced by fiber components are not common for lightin reference and sample paths. Therefore, at the output of thefiber-based polarization-sensitive Michelson, Mach-Zehnder or similarhybrid interferometers, recorded interference fringe signals may containan unknown time-varying random phase factor due to polarization changesinduced by fiber components.

The embodiments described herein solve these problems, as well asothers.

SUMMARY OF THE INVENTION

The foregoing and other features and advantages are defined by theappended claims. The following detailed description of exemplaryembodiments, read in conjunction with the accompanying drawings ismerely illustrative rather than limiting, the scope being defined by theappended claims and equivalents thereof.

A method and apparatus for analyzing a sample. The method and apparatusdetermines depth-resolved polarization properties of the sample. In oneembodiment is a spectral interferometer for analyzing a sample. Theinterferometer comprises a light source which produces light over amultiplicity of optical frequencies. The interferometer comprises ananalyzer that records the intensity of light at the output of theinterferometer. The interferometer comprises at least one optical fiberthrough which the light is transmitted to the sample. The interferometercomprises a receiver which receives the light reflected from the sample.A computer coupled to the interferometer determines depth-resolvedpolarization properties of the sample.

Another embodiment pertains to a method for analyzing a sample with aspectral interferometer. The method comprises the steps of directinglight to the sample with at least one optical fiber of theinterferometer. There is the step of reflecting the light from thesample. There is the step of receiving the light with a receiver of theinterferometer. There is the step of determining depth and polarizationproperties of the light reflected from the sample with a computercoupled to of the interferometer.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing description of the figures is provided for a more completeunderstanding of the drawings. It should be understood, however, thatthe embodiments are not limited to the precise arrangements andconfigurations shown.

FIG. 1 is a schematic diagram of a polarization-sensitive spectralinterferometer in accordance with one embodiment.

FIG. 2 a schematic diagram of a PS-OCT interferometer in accordance withone embodiment.

FIG. 3A depicts the typical spectral output intensity from the fiberbased single channel polarization-sensitive spectral interferometer withthe whole spectrum of 12.2 THz.

FIG. 3B depicts an enlarged small segment of 10 GHz between 190.69 THzand 190.79 THz of the whole spectrum (12.2 THz) from FIG. 2A to viewfringes in more detail.

FIG. 4A depicts the Fourier Transform magnitude of interference fringesbetween and from the back surfaces of the glass window.

FIG. 4B depicts the Fourier Transform magnitude of interference fringesbetween the back surface of the glass window and the birefringentsample.

FIG. 5A depicts Phase retardation due to birefringence of thebirefringent sample estimated from interference between the back surfaceof the glass window and the back surface of the birefringent sample.

FIG. 5B depicts Phase Retardation due to fast-axis angle of thebirefringent sample estimated from interference between the back surfaceof the glass window and the back surface of the birefringent sample.

FIG. 6 is a schematic of the origin of form-birefringence (Δn) andform-biattenuance (Δ_(χ)) in fibrous structures, where the electricfield of incident light which is polarized perpendicular to the fiberaxis (Ε_(⊥)) produces a surface charge density with an induced field(Ε_(o)), which changes the dielectric susceptibility and gives higherrefractive index (n_(s)) relative to that experienced by light polarizedparallel to the fiber axis (Ε_(∥)).

FIG. 7 is a schematic model for form-biattenuance consisting ofalternating anisotropic and isotropic layers.

FIG. 8 is a schematic of intervertebral disc and annulus fibrosisshowing alternating fiber directions in the laboratory frame (H and V),the incident beam, and scan location (dashed red line).

FIG. 9A is a Poincaré sphere showing the simulated trajectory ofS(z_(j)) for k=3 layers with fiber orientations θ=−10°, 95°, and −5°;and FIG. 9B is a graph of the abrupt changes in trajectory of S(z_(j))corresponding to layer interfaces at z_(j)=34 and z_(j)=70 are observedas spikes in the curvature [κ(z)] indicated by dashed circles.

FIG. 10A is a graph of the ensemble averaging N_(A) uncorrelated specklefields increases PSNR by a factor of N_(A1/2), and FIG. 10B is aPoincaré sphere before (thin line) and after (thick line) averagingN_(A)=36 speckle fields for birefringent film S_(m)(z) for m=1 plottedon the Poincaré sphere. Averaged S(z) begins to resemble the noise-freemodel polarization arc P(z).

FIG. 11A is a Poincaré sphere showing depth-resolved polarization data[S_(m)(z), gray] for M=6 incident polarization states in a thick (Δz=170μm) RNFL 1 mm inferior to the ONH; and FIG. 11B is a Poincaré sphereshowing thin (Δz=50 μm) RNFL 1 mm nasal to the ONH. Noise-free modelpolarization arcs [P_(m)(z), black] and rotation axis (A) were extractedby the multi-state nonlinear algorithm. (Note: m=3, 4, and 5 are on thefar side of the Poincaré sphere.)

FIG. 12 is a graph of the RNFL birefringence (Δn) in locations 1 mminferior and 1 mm nasal to the center of the ONH on two separate days,where the error bars indicate approximate PS-OCT birefringencesensitivity.

FIG. 13A is a Poincaré sphere showing the depth-resolved polarizationdata [S₁(z)] and associated noise-free model polarization arc [P₁(z)]and eigen-axis ({circumflex over (β)}) determined by the multistatenonlinear algorithm in rat tail tendon with relatively highform-biattenuance (Δ_(χ)=8.0·10⁻⁴); and FIG. 13B is a graph for thecorresponding normalized Stokes parameters [Q(z), U(z), V(z)] andassociated nonlinear fits.

FIG. 14A is a Poincaré sphere showing the depth-resolved polarizationdata [S₁(z)] and associated noise-free model polarization arc [P₁(z)]and eigen-axis ({circumflex over (β)}) determined by the multistatenonlinear algorithm in rat tail tendon with relatively lowform-biattenuance (Δ_(χ)=3.0·10⁻⁴); and FIG. 14B is a graph for thecorresponding normalized Stokes parameters [Q(z), U(z), V(z)] andassociated nonlinear fits.

FIG. 15A is a Poincaré sphere showing S₁(z) and associated P₁(z) and{circumflex over (β)} determined by the multistate nonlinear algorithmin rat Achilles tendon; and FIG. 15B is the corresponding normalizedStokes parameters of FIG. 15A and associated nonlinear fits.

FIG. 16A is a Poincaré sphere showing the S_(m)(z) and associatedP_(m)(z) and {circumflex over (β)} for in vivo primate RNFL for M=6; andFIG. 16B is the corresponding normalized Stokes parameters [Q(z), U(z),V(z)] and associated nonlinear fits are shown for a single incidentpolarization state (m=1).

FIG. 17 is an intensity B-scan of annulus fibrous, the image is 0.35 mmwide, 0.5 mm deep, and intensity is plotted logarithmically usingarbitrary units.

FIG. 18A is a Poincaré sphere with the trajectory of S_(m)(z) forannulus fibrous; and FIG. 18B is a graph of the abrupt changes intrajectory of S_(m)(z) corresponding to lamellar interfaces atz=z_(top)+Δz₁ and z=z_(top)+Δz₁+Δz₂ are observed as spikes in thecurvature [κ(z)] indicated by circles.

FIG. 19 a fiber orientation B-scan [θ(x,z)] of the annulus fibrousspecimen shown in FIG. 17, where the fiber orientation (θ) is assigned afalse color representing the counterclockwise angle between the fiberaxis and the horizontal as viewed along the incident beam.

FIG. 20 is a PS-OCT birefringence B-scan [Δn(x,z)] of the annulusfibrous specimen shown in FIG. 17, where the detected interfaces betweenlamellae are represented by black lines.

FIG. 21 is an intensity B-scan [I(x,z)] introduced in FIG. 17 with blacklines superimposed to indicate structural features (lamellar interfaces)that were not apparent in I(x,z) but were detected in the depth-resolvedpolarization data [S_(m)(z)], where the numbers on left represent meanthickness of each lamella (Δ_(k), μm).

DETAILED DESCRIPTION OF THE EMBODIMENTS

The methods, apparatuses, and systems can be understood more readily byreference to the following detailed description of the methods,apparatuses, and systems, and the following description of the Figures.

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIGS. 1 and 2 thereof, there is shown a polarizationsensitive spectral interferometer for analyzing a sample. Polarizationsensitive spectral interferometer and polarization sensitive OpticalCoherence Tomography (“PS-OCT”) may be used interchangeably throughoutthe application. PS-OCT combines polarimetric sensitivity with the highresolution tomographic capability of optical coherence tomography(“OCT”) to determine phase retardation (δ) and birefringence (Δn)biattenuance (Δ_(χ)) and optical axis orientation (θ). In oneembodiment, the PS-OCT configuration includes an interferometer and alight source which produces light over a multiplicity of opticalfrequencies. The interferometer comprises at least one optical fiberthrough which the light is transmitted to the sample. The interferometercomprises a receiver which receives the light reflected from the sample.The interferometer comprises a computer coupled to the receiver whichdetermines depth-resolved polarimetric properties of the sample.“Depth-resolved” is may be used in the context of either measuring inthe depth dimension or the local variation in a parameter versus depth[e.g., Δ_(χ)(z)]”.

In one embodiment, the computer coupled to the interferometer determinessimultaneously the depth-resolved polarimetric properties of the lightreflected from the sample in the interferometer. In another embodiment,the computer determines variations of the polarization of the reflectedlight as a function of depth of the sample. In another embodiment, thecomputer determines the depth resolved birefringence of the sample,depth resolved retardation of the sample, depth resolved biattenuance ofthe sample, and depth resolved optical axis of the sample. The sample ispreferably living human tissue, and the reflected light is obtained invivo in a patient, as described in U.S. patent application Ser. No.11/466,683 and U.S. patent application Ser. No. 10/548,982, both ofwhich are incorporated by reference herein. The computer preferablyidentifies tissue type of the sample as a function of depth from thedepth-resolved birefringence, retardation, biattenuance and optical axisof the sample. For instance, by maintaining a table look-up in a memoryof the computer having a priori information regarding tissue types andtheir associated birefringence, retardation, biattenuance, and opticalaxis properties; when unknown tissue is tested using the techniquesdescribed herein, the birefringence, biattenuance, retardation, andoptical axis properties obtained as a function of depth of the unknowntissue is compared with the known information in the table look-up, andthe tissue type as a function of depth is identified. Tissues mayinclude any type of tissue including, but not limited to, arterialvessels and plaques, amyloid plaques and neurofibrillary tangles,aneurysms, urethra, tumors, cartilage, cornea, muscle, retina, nerve,skin and tendon. Alternatively, a follow-up PS-OCT measurement may beemployed, looking for changes in birefringence, biattenuance,retardation, and optical axis with the previous measurement(s).Alternatively, the sample may be an optical fiber or general opticalelement transmitting device under test.

Another embodiment pertains to a method for analyzing a sample with aspectral interferometer. The method comprises the steps of directinglight to the sample with at least one optical fiber of theinterferometer. There is the step of reflecting the light from thesample. There is the step of receiving the light with a receiver of theinterferometer. There is a step of combining or interfering the lightreflected from the sample with the light reflected from the referencesurface. There is the step of determining depth and polarizationproperties of the light reflected from the sample with a computer of theinterferometer.

In one embodiment, the determining step includes the step of determiningsimultaneously the depth-resolved polarimetric properties of the lightreflected from the sample with the computer. The determining steppreferably includes the step of determining variations of thepolarization of the reflected light as a function of depth of thesample. Preferably, the determining step includes the step ofdetermining depth resolved birefringence of the sample, depth resolvedbiattenuance of the sample, depth resolved retardation, and depthresolved optical axis of the sample. There is preferably the step ofidentifying tissue type of the sample as a function of depth from thedepth-resolved birefringence, depth-resolved biattenuance,depth-resolved retardation, and depth-resolved optical axis.

In another embodiment, a polarization-sensitive spectral interferometergenerally comprising a broadband frequency-swept laser source, anoptical spectrum analyzer (“OSA”), a fiber-based common-path spectralinterferometer coupled with a fiber-optic spectral polarimetryinstrument (“FOSPI”) in the detection path, and photoreceiver. Thefiber-based single channel polarization spectral interferometer providesdepth resolved measurement of polarization transformations of lightreflected from a sample. The range of detectable optical path-lengthdifference using spectral interferometry is proportional to the inverseresolution of the OSA. Algebraic expressions for the Stokes parametersor alternative measure of the polarization state of light—Jones vectoror complex Z-parameter, at the output of the interferometer are derivedfor light reflected from a birefringent sample by using thecross-spectral density function. By insertion of the fiber opticspectral polarimetry instrument into the detection path of a common pathspectral interferometer, the full set of Stokes parameters of lightreflected from a sample can be obtained with a single optical frequencyscan—or improved estimates by averaging multiple optical frequencyscans. This embodiment requires neither polarization control componentsnor prior knowledge of the polarization state of light incident on thesample.

In another embodiment, the interferometer comprises a polarimeter withchanneled spectra in spectral polarimetry without polarization control.The polarimeter comprises of a pair of thick birefringent retarders inseries with a polarizer and OSA, and a fiber optic spectral polarimetryinstrument to measure polarization state of collected light with singleoptical frequency scan utilizing the principle of the channeled spectralpolarimetry. Alternatively, the polarimeter comprises polarizationsensitivity that records four sequential single-channel measurements orsimultaneous dual-channel horizontal and vertical polarization componentmeasurements in conjunction with a well characterized reference beam.The polarimeter may be utilized to measure the polarization state oflight or sample birefringence.

In another embodiment, the fiber-based polarization-sensitive Michelson,Mach Zehnder or similar hybrid interferometer extracts the Stokesparameters of reflected light from a sample from the interference fringesignal recorded in two orthogonal polarization channels. The recordedinterference fringe signal includes the phase difference between lightreflected from the reference and sample surfaces as well as amplitudes,so polarization-state control of light reflected form the referencesurface may be employed. In the common-path spectral interferometer, thephase factor due to polarization changes induced by fiber components iscommon in light reflected from reference and sample surfaces and cancelsin the interference fringe signals recorded in orthogonal channels. Inthe PS-OCT configurations, the interferometer determines the depthresolved birefringence of the sample, depth resolved retardation of thesample, depth resolved biattenuance of the sample, and depth resolvedoptical axis of the sample.

Retardation and Birefringence

PS-OCT combines polarimetric sensitivity with the high resolutiontomographic capability of optical coherence tomography (“OCT”) todetermine phase retardation (δ) and birefringence (Δn) biattenuance(Δ_(χ)) and optical axis orientation (θ). Noninvasive and invasivedetermination of δ, Δn, Δ_(χ), and θ in biological tissue makes thePS-OCT configurations well-suited for clinical diagnostics andbiomedical research applications where monitoring of tissue isimportant. Optical anisotropy properties birefringence (Δn),biattenuance (Δ_(χ)), and axis orientation (θ) convey information aboutthe sub-microscopic structure of fibrous tissue (e.g., connective,muscle, nervous tissue, fibrous cap, and the like).

A primary obstacle to high sensitivity determination of tissueretardation and birefringence is polarimetric speckle noise. Specklenoise is common to all imaging modalities that employ spatially-coherentwaves (e.g. ultrasound, radar, OCT, etc.). The method to determineaccurately polarimetric properties addresses the degrading effects ofspeckle noise in polarimetric signals detected with PS-OCTconfigurations. The method comprises the sensitivity required foraccurate determination of δ, Δn, Δ_(χ), and θ in thin tissues with weakbirefringence [e.g., primate retinal nerve fiber layer (“RNFL”),Δn×10⁻⁴] and/or biattenuance.

The method to determine δ, Δn, Δ_(χ), and θ comprises multiple incidentpolarization states and a nonlinear fitting algorithm to determine δ,Δn, Δ_(χ), and θ with high sensitivity and invariance to unknownincident unitary polarization transformations that may occur in theinterferometer. In one example, the “multi-state nonlinear algorithm” isdemonstrated in a thin turbid birefringent film.

Form-Biattenuance (Δn) and Form-Birefringence (Δ_(χ))

Form-birefringence (Δn) in tissue arises from anisotropic lightscattering by ordered submicroscopic cylindrical structures (e.g.,microtubules, collagen fibrils, etc.) whose diameter is smaller than thewavelength of incident light but larger than the dimension of molecules.Inasmuch as form-birefringence (Δn) describes the effect of differentialphase velocities between light polarized parallel- and perpendicular-tothe fiber axis (eigenpolarizations), the term form biattenuance (Δ_(χ))describes the related effect of differential attenuation oneigenpolarization amplitudes. Biattenuance (Δ_(χ)) is an intrinsicphysical property responsible for polarization-dependent amplitudeattenuation, just as birefringence (Δn) is the physical propertyresponsible for polarization-dependent phase delay. Diattenuation (D)gives the quantity of accumulated anisotropic attenuation over a givendepth (Δz) by a given optical element.

Optical Axis

Optic axis orientation (θ) provides the direction of constituent fibersrelative to a fixed reference direction (i.e., horizontal in thelaboratory frame). The PS-OCT configurations measures depth-resolvedoptic axis orientation [θ(z)] deep within multiple layered tissue using.Using the PS-OCT configurations, the depth-resolved optic axisorientation [θ(z)] unambiguously represents the actual anatomical fiberdirection in each layer or depth (z) with respect to a fixed laboratoryreference and can be measured with high sensitivity and accuracy.Characterization of the anatomical fiber direction in connective tissueswith respect to a fixed reference is important because functional andstructural characteristics such as tensile and compressive strength aredirectly related to the orientation of constituent collagen fibers.

Depth Resolved Identification of Structural interfaces

Depth-resolved curvature (κ(z)) of normalized Stokes vectors (S(z)) mayidentify boundaries in multiple-layered fibrous tissue. When contrast inbackscattered intensity (I(z)) is not sufficient for identification oflamellar interfaces, the PS-OCT configurations can detect changes indepth-resolved fiber orientation and increases image contrast inmultiple layered birefringent tissues. For example, interfaces in theannulus fibrous identified using depth-resolved fiber orientation or thedepth-resolved curvature allowed quantification of lamellae thickness.Moreover, the PS-OCT configuration can detect changes in fiberorientation without intense processing needed to effectively quantifytissue retardation and diattenuation.

Cytoskeletal elements, cell membranes, and interstitial collagen impartform-birefringence to tissues such as arterial vessels, amyloid plaques,aneurysms, tumors, cartilage, cornea, muscle, urethra, nerve, retina,skin and tendon. Noninvasive and invasive quantification ofform-birefringence, retardation, and optical axis by the PS-OCTconfigurations 10 and 200 has implications in the clinical managementand basic understanding of diseases including but not limited toosteoarthritis, myocardial heart disease, thyroid disease, aneurism,gout, Alzheimer's disease, cancers, tumors, glaucoma, and chronicmyeloid leukemia. In addition, changes in form-birefringence mayelucidate traumatic, functional, or physiologic alterations such as theseverity and depth of burns; wound healing, optical clearing byexogenous chemical agents, or the contractile state of muscle.

Exemplary Polarization Sensitive Spectral Interferometer Configuration

As shown in FIG. 1, in one configuration of the PS-OCT system is apolarization-sensitive spectral interferometer 10 generally comprising abroadband frequency-swept laser source 12, an Optical Spectrum Analyzer(“OSA”) 14, a fiber-based common-path spectral interferometer 30, aFiber-Optic Spectral Polarimetry Instrument (“FOSPI”) 50, and aphotoreceiver 60. In one embodiment, the broadband frequency-swept lasersource 10 operates with a mean frequency of the output spectrum thatvaries over time. The swept laser source may be any tunable laser sourcethat rapidly tunes a narrowband source through a broad opticalbandwidth. The tuning range of the swept source may have a tuning rangewith a center wavelength between approximately 500 nanometers and 2000nm, a tuning width of approximately greater than 1% of the centerwavelength, and an instantaneous line width of less than approximately10% of the tuning range with an instantaneous coherence length of over10 mm. The mean frequency of light emitted from the swept source maychange continuously over time at a tuning speed that is greater than 100terahertz per millisecond and repeatedly with a repetition period. TheOSA 14 provides real-time OSA or a clock signal 18 that is used totrigger data acquisition for real-time synchronization of outputintensity with optical frequency (v) 16. High spectral resolution of thelaser source (or alternatively long coherence length) 12 and the OSA 14can provide a scan range greater than 10 mm and up to 3 m and allows aflexible system configuration, such as a reference-sample separation upto several centimeters. Selecting optimal optics for the frequency rangeof the broadband frequency-swept laser source 12 is readily known bythose skilled in the art. In one embodiment, the narrowband laser source12 is swept the over a wide optical frequency range and the opticalfrequency 16 is optically coupled to a processor 70. Thepolarization-sensitive spectral interferometer 10 may be based onoptical fibers for optically coupling the components thereof.

As shown in FIG. 1, in one embodiment, the swept laser source 12 isoptically coupled to an input polarization state preparation optics 20,comprising a lens 22 and a polarizing element 24. The input polarizationoptics preparation optics 20 allows the preparation of a variety offixed user-specified states. The light then collected by a lens 26 andtransmitted to the fiber circulator 28. The sample and reference beamsshare a common path 38 in the spectral interferometer 10. Thisconfiguration provides automatic compensation for dispersion andpolarization difference in the sample and reference paths up to thesample and nearly ideal spatial overlap of reflected sample andreference beams, giving high fringe visibility.

FIG. 1 depicts one embodiment of the common-path spectral interferometer30 including, the fiber optic circulator 28, a lens 32, a glass window34 as a reference, and a sample 36 in a common path 38. Emitted lightfrom the source 12 is transmitted to the fiber optic circulator 28,which prevents any unnecessary light loss returning to the source 12 soa fiber based system can be implemented. Emitted light inserted into oneport of the circulator 28 is transmitted to a center tap, while thereflected light from the glass window 16 reference and sample 18 istransmitted to the third port of the circulator 22 to a detection path40. The back surface of the glass window 34 serves as a referencesurface. The thickness of the glass window 34 is large enough, so thatreflection from the front surface of the glass window does notcontribute to the spectral interferogram between light reflected fromthe reference and that reflected from the sample. In one embodiment, aborosilicate glass window of 6.3 mm thickness is used. In oneembodiment, an end facet of the sample path illuminating fiber insteadof the glass window 34 can be used in the sample path.

Alternatively, the sample path can be coupled to a probe or catheter viaa fiber optic rotary junction. Examples of a rotating catheter tip forthe sample path include, a Catheter for In Vivo Imaging as described in60/949,511, filed Jul. 12, 2007, or an OCT catheter as described inProvisional Application Ser. No. 61/051,340, filed May 7, 2008, eachherein incorporated by reference for the methods, apparatuses andsystems taught therein. The catheter 242 can be located within a subjectto allow light reflection off of subject tissues to obtain opticalmeasurements, medical diagnosis, treatment, and the like. The reference16 can be coupled to a reflective surface of a ferrule coupled to a lensand rotating prism to provide the common path 38.

Data acquisition is synchronized with calibrated optical clocktransitions generated by the OSA 14, so each measured and digitizedlight intensity corresponds to uniformly spaced or a known opticalfrequency or spectral component of the spectral interferogram inequation (1).

W _(ij)(r,r,v)=W _(ij) ⁽¹⁾(r,r,v)+W _(ij) ⁽²⁾(r,r,v)+2R{W _(ij)(r ₁ ,r ₂,v)e ^(i2Πντ) },i=j  (1)

Equation (1) includes autocorrelation terms that arise from interferencebetween surfaces within the sample are not shown. Autocorrelations termscan appear as artifacts and coherent noise; they can be separated fromthe interference term between the reference and the sample containinguseful depth information by shifting the reference and sample containinguseful depth information by shifting the reference surface by a distancelarger than the sample optical thickness.

F ⁻¹ {W _(ij)(r,r,v)}=F ⁻¹ {W _(ij) ⁽¹⁾(r,r,v)}+F ⁻¹ {W _(ij)⁽²⁾(r,r,v)}+Γ_(ii)(r ₁ ,r ₂ ,t−τ)+Γ*_(ii)(r ₁ ,r ₂ ,t+τ).  (2)

With equation (2), interference fringes can be analyzed by a Fouriertransform of the recorded spectrum. Equation (2) is the inverse Fouriertransform of Equation (1) with respect to optical frequency v.

As shown in FIG. 1, the detection path 40 includes a firstPolarization-Maintaining (“PM”) fiber segment 42, a second PM fibersegment 44, and a polarization controller 46 coupled to the FOSPI 50.The first and second PM fibers 42 and 44 are spliced at 45 degrees withrespect to each other. The PM fibers are a birefringent opticalwaveguide that has two orthogonal axes with different refractive indicesdue to internal stress structures. The first and second PM fibersegments 42 and 44 are used as sequential linear retarders in a retardersystem. In one embodiment, the first PM fiber 42 is 2.5 m and the secondPM fiber 44 is 5 m. In another embodiment, the use of longer PM fibersegments would allow wider channel separation and provide betterestimates of sample phase retardation and fast-axis orientation. The PMfibers are thermally isolated in mechanical enclosures to improve thestability of PM fiber phase retardations. Orthogonal oscillating fieldcomponents of collected light experience different phase delays due tointernal birefringence while passing through the first PM fiber segment42. At the 45 degree splice 44, both oscillating field components areprojected equally on fast and slow axes of the second PM fiber segment44 and experience different phase delays. Light exiting the second PMfiber 44 segment has four field components with different phase delaysdepending on the propagation path and passes through an analyzer 36aligned with the fast axis of the first PM fiber segment 42. All fourfield components of light are projected onto the transmission axis ofthe analyzer 36 and produce interference fringes with characteristictime delay (τ) given by the PM fiber segments 42 and 44. In oneembodiment, the use of thermally isolated mechanical enclosure improvesthe stability of PM fiber phase retardations. In one embodiment, the useof longer PM fiber segments allows wider channel separation and providesbetter estimates of sample phase retardation and fast-axis orientation.The FOSPI is but one implementation of an apparatus to accomplishinterference between the different polarization states. Bulk opticalelements may accomplish more or less the same objective of the FOSPI.Bulk components may include better stability but the size ranges ofoptical delays that can be realized are limited, as described in K. Okaand T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt.Lett. 24: 1475-1477 (1999), herein incorporated by reference.

The FOSPI 50 includes an analyzer 52 coupled to a photoreceiver 60. Inone embodiment, the analyzer 52 includes a collimating lens 54, apolarizer 56, and a lens 58. In operation, output intensity from thecommon-path spectral interferometer 30 is collected by the FOSPI 50,which is then coupled into the photoreceiver 60 and then input into ananalog-to-digital converter 62 that acquires output intensity data by aprocessor 70 under a LabView™ software interface. By insertion of theFOSPI 50 in the detection path of a common-path spectral interferometer30, the full set of Stokes parameters of light backscattered fromspecific sample depths can be obtained without eitherpolarization-control components in the reference, sample, or detectionpaths of the interferometer or prior knowledge of the polarization stateof light incident on the sample. The OSA 14 provides real-time OSA orclock signal 18 that is used to trigger data acquisition for real-timesynchronization of output intensity with optical frequency (v).

Output spectral intensity [I_(out) (v)] at optical frequency v emergingfrom the FOSPI is:

I _(out)(v)=½S _(0,in)(v)+½ cos φ₂ S _(1,in)(v)+½ sin φ₁(v)sin φ₂(ν)S_(2,in)(v)−½ cos φ₁(v)sin φ₂(ν)S _(3,in)(v)=½S _(0,in)(v)+½ cos φ₂(v)S_(1,in)(v)+¼|S _(23,in)(v)|cos(φ₂(v)−φ₁(v)+arg(S _(23,in)(v))−¼|S_(23,in)(v)cos(φ₂(v)+φ₁(v)−arg(S _(23,in)(v))  (3)

with S_(0,in)(v), S_(1,in)(v), and S_(23,in)(v)=S_(2,in)(v)−iS_(3,in)(v)representing Stokes spectra of collected light (i.e., incident on thefirst PM fiber segment 32). The fiber coordinate system utilized torepresent the Stokes spectra is oriented so that light oscillating alongthe fast axis of the first PM fiber segment 34 corresponds to S₁=1. Hereφ₁(v) and φ₂(v) are the phase retardations due to the first and secondsegments of the PM Fiber 42 and 44 and dependent on optical frequency v,

$\begin{matrix}{{{\varphi_{1{(2)}}(v)} = {\frac{2\; \Pi \; v\; \Delta \; {n(v)}}{c}L_{1{(12)}}}},} & (4)\end{matrix}$

where Δn(v) is internal birefringence of the PM fiber.

From Equation (3), the output intensity from the FOSPI [I_(out)(v)] is asuperposition of four Stokes spectra [S_(0,in)(v), S_(1,in)(v), andS_(23,in)(v)=S_(2,in)(v)−iS_(3,in)(v)] modulated at different carrierfrequencies dependent on phase retardations [φ₁(v) and φ₂(v)] in the PMfiber segments. Simple Fourier transformation of I_(out)(v) isolateseach Stokes spectral component in the time-delay domain (τ) or opticalpath length difference (cτ) domain. Subsequent demodulation of each peakin the time-delay domain provides the complete set of Stokes spectra[S_(0,in)(v), S_(1,in)(v), S_(2,in)(v), S_(3,in)(v)].

When the FOSPI is placed in the detection path of a common path spectralinterferometer, two factors determine the spectral modulation. One isthe optical path-length difference between reference and samplesurfaces, Δ(v), introduced by the common-path spectral interferometer,and the other factor is the phase retardations, φ₁(v) and φ₂(v),generated by the retarder system in the FOSPI. These two factors combinesequentially so that output from the fiber based single channelpolarization sensitive spectral interferometer is a convolution of theFOSPI output and that from the common path spectral interferometer.

Computation of the Output Intensity of Interfering Light

When a FOSPI is connected to the detection path of a common pathspectral interferometer, an expression for the output intensity ofinterfering light can be derived. With Equations (25) and (28), measuredinterference fringe intensity of light from the common path spectralinterferometer passing through the FOSPI after reflecting from abirefringent sample is:

$\begin{matrix}{{I_{out}^{(i)}(v)} = {{r_{s}\cos \; \Delta \; (v)\cos \frac{\delta (v)}{2}{S_{0}^{(1)}(v)}} + {r_{s}\sin \; \Delta \; \left( {v\; \sin} \right)\frac{\delta \; (v)}{2}\left( {{{co}\; 2\; \alpha \; {S^{(1)}(v)}} + {\sin \; 2\; \alpha \; {S_{s}^{(1)}(v)}}} \right)} + {\frac{1}{2}{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{1}^{(1)}(v)}} - {\sin \frac{\delta \; (v)}{2}\sin \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta \; (v)} - {\varphi_{2}(v)}} \right)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{0}^{(1)}(v)} \times {\sin \left( {{\Delta \; (v)} - {\varphi_{2}(v)}} \right)}}} \right\rbrack}} + {\frac{1}{2}{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{1}^{(1)}(v)}} - {\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta \; (v)} - {\varphi_{2}(v)}} \right)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{0}^{(1)}(v)} \times {\sin \left( {{\Delta (v)} - {\varphi_{2}(v)}} \right)}}} \right\rbrack}} + {\frac{1}{4}{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{2}^{(1)}(v)}} - {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta \; (v)} - {\varphi_{2}(v)} + {\varphi_{1}(v)}} \right)}} + {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; S_{0}^{(1)} \times (v)} + {S_{1}^{(1)}(v)} - {\sin \frac{\delta (v)}{2}\cos \; 2\alpha \; {S_{2}^{(1)}(v)}} + {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right\} {\sin \left( {{\Delta (v)} - {\varphi_{2}(v)} + {\varphi_{1}(v)}} \right)}}} \right\rbrack}} + {\frac{1}{4}{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{2}^{(1)}(v)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta (v)} + {\varphi_{2}(v)} - {\varphi_{1}(v)}} \right)}} + {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\alpha \; S_{0}^{(1)} \times (v)} - {S_{1}^{(1)}(v)} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{2}^{(1)}(v)}} - {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right\} {\sin \left( {{\Delta (v)} + {\varphi_{2}(v)} - {\varphi_{1}(v)}} \right)}}} \right\rbrack}} - {\frac{1}{4}{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{2}^{(1)}(v)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta \; (v)} - {\varphi_{2}(v)} - {\varphi_{1}(v)}} \right)}} - {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; S_{0}^{(1)} \times (v)} - {S_{1}^{(1)}(v)} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{2}^{(1)}(v)}} - {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right\} {\sin \left( {{\Delta \; (v)} - {\varphi_{2}(v)} - {\varphi_{1}(v)}} \right)}}} \right\rbrack}} - {\frac{1}{4}{{r_{s}\left\lbrack {{\left( {{\cos \frac{\delta (v)}{2}{S_{2}^{(1)}(v)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) \times {\cos \left( {{\Delta \; (v)} + {\varphi_{2}(v)} + {\varphi_{1}(v)}} \right)}} + {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; S_{0}^{(1)} \times (v)} + {S_{1}^{(1)}(v)} - {\sin \frac{\delta (v)}{2}\cos \; 2\alpha \; {S_{2}^{(1)}(v)}} + {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right\} {\sin \left( {{\Delta \; (v)} - {\varphi_{2}(v)} - {\varphi_{1}(v)}} \right)}}} \right\rbrack}.}}}} & (5)\end{matrix}$

A Fourier transform of Equation (5) gives seven components for eachbackreflection of light in the positive optical path-length differencedomain (cπ>0), which are centered at cL_(o), c(L_(o)±l_(2,o)),c(L_(o)±(l_(2,o)l_(1,o))), and c(L_(o)±(l_(2,o)+l_(1,o))), respectively,with Δ(v)=2ΠL_(o)v+2ΠL₁(v), φ_(i)(v)=2Πl_(i,o)v+2ΠL_(i,1)(v).

By computing an inverse Fourier transform of each isolated component inthe optical path-length difference domain (cτ), Equations (6-9) areobtained:

$\begin{matrix}{{L_{o}:{\frac{1}{2}r_{s}^{\; \Delta \; {(\upsilon)}}\left\{ {{\cos \frac{\delta (v)}{2}{S_{0}^{(1)}(\upsilon)}} - {\; \sin \frac{\delta (\upsilon)}{2}\left( {{\cos \; 2\; \alpha \; {S_{1}^{(1)}(\upsilon)}} + {\sin \; 2\; \alpha \; {S_{2}^{(1)}(\upsilon)}}} \right)}} \right\}}},} & (6) \\{\left. {L_{o} + {I_{2,o}:{\frac{1}{4}r_{s}^{{\varphi}_{2}}^{{\; {\Delta {(\upsilon)}}}\;}\left\{ {\left( {{\cos \frac{\delta (v)}{2}{S_{1}^{(1)}(v)}} - {\sin \frac{\delta (v)}{2} \times \sin \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) - {\; \sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{0}^{(1)}(v)}}} \right)}}} \right\},} & (7) \\\left. \left. {L_{o} + l_{2,o} - {l_{1,0}:{\frac{1}{8}r_{s}^{{({{\varphi_{2}{(\upsilon)}} - {\varphi_{1}{(\upsilon)}}})}}{^{\; {\Delta {(\upsilon)}}}\left\lbrack {\left( {{\cos \frac{\delta (v)}{2}{S_{1}^{(1)}(v)}} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) - {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; {S_{0}^{(1)}(v)}} - {S_{1}^{(1)}(v)}} \right)} + {\sin \frac{\delta (v)}{2}\cos \; 2\alpha \; {S_{2}^{(1)}(v)}} - {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right)}}}} \right\} \right\rbrack & (8) \\\left. \left. {L_{o} + l_{2,o} - {l_{1,0}:{{- \frac{1}{8}}r_{s}^{{({{\varphi_{2}{(\upsilon)}} + {\varphi_{1}{(\upsilon)}}})}}{^{{\Delta}{(\upsilon)}}\left\lbrack {\left( {{\cos \frac{\delta (v)}{2}S\; 2^{(1)}(v)} + {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{3}^{(1)}(v)}}} \right) - {\left\{ {{\sin \frac{\delta (v)}{2}\sin \; 2\alpha \; {S_{0}^{(1)}(v)}} + {S_{1}^{(1)}(v)}} \right)} - {\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{2}^{(1)}(v)}} + {\cos \frac{\delta (v)}{2}{S_{3}^{(1)}(v)}}} \right)}}}} \right\} \right\rbrack & (9)\end{matrix}$

The real part of expression (6) gives S₀ ^((i))(v)/4, and the real partof expression (7), after the phase shift by −φ₂(v), gives S₁ ⁽¹⁾(v)/8.Likewise, S₂ ⁽¹⁾(v)/8 and S₃ ⁽¹⁾(v)/8 is obtained by taking the realpart of the subtraction of expression (9) from expression (8) and theimaginary part of the sum of expressions (8) and (9) after theappropriate phase shift from the FOSPI, −φ₂(v)−φ₁(v)) and −φ₂(v)+φ₁(v))for expressions (8) and (9), respectively. Since the phase retardationsφ₁(v) and φ₂(v) depend only on the length and birefringence of PM fibersegments, they are calibrated regardless of the unknown polarizationcharacteristics of the sample and polarization state of incident light.

Simple arithmetic gives sample phase retardation (δ) due to thebirefringence and the fast axis (α or θ)) angle without knowledge of theincident polarization state. The real part of expression (6), theimaginary part of expression (7), and the imaginary part after thesubtraction of expression (8) from expression (9) are:

$\begin{matrix}{{\frac{1}{2}r_{s}\cos \frac{\delta (v)}{2}{S_{0}^{(1)}(v)}},} & (10) \\{{\frac{1}{4}r_{s}\sin \frac{\delta (v)}{2}\cos \; 2\; \alpha \; {S_{0}^{(1)}(v)}},} & (11) \\{{\frac{1}{4}r_{s}\sin \frac{\delta (v)}{2}\sin \; 2\; \alpha \; {S_{0}^{(1)}(v)}},} & (12)\end{matrix}$

after phase shifts by −Δ(v).−(Δ(v)+φ₂(v)), −(Δ(v)+φ₂(v)−φ₁(v)), and−(Δ(v)+φ₂(v)+φ₁(v)), respectively. Δ(v) can be obtained from thelocation of the S₀ ^((i)) component in the optical path-lengthdifference domain, assuming dispersion in the sample is small. With atrigonometric identity, Equation (13) is obtained:

$\begin{matrix}{{{\tan \frac{\delta (v)}{2}} = \frac{2\sqrt{{{expression}(36)}^{2} + {{expression}(37)}^{2}}}{{expression}(35)}},} & (13) \\{{\tan \; \alpha} = {\frac{{expression}(37)}{{expression}(36)}.}} & (14)\end{matrix}$

In this analysis, sample phase retardation (δ(z)) and fast-axis angle (αor θ) can be estimated with the interference fringes and withoutknowledge of the polarization state of the incident light. When thepolarization optics is inserted between the reference and the samplesurfaces, the segment can be considered a known portion of thebirefringent sample with a specified polarization transformation, andthe analysis may be modified to determine the depth-resolvedbirefringence (Δn) and fast axis (α or θ) of a sample, as explained inthe Optical Axis and Birefringence sections below.

Exemplary PS-OCT Configuration

As shown in FIG. 2, another embodiment of the PS-OCT system cancomprise, a Mach-Zehnder interferometer in a PS-OCT configuration 200,which measures the complex mutual coherence function (magnitude andphase) between two non-reciprocal optical paths, one path encompassingan object under test (i.e. “the sample”) and the other a reference path.This is in contrast to a Michelson interferometer configuration whichmeasures the same coherence function in a reciprocal configuration (i.e.the same splitter/coupler is used for both input splitting and outputrecombination). Alternatively, the PS-OCT interferometer can comprise aMichelson interferometer configuration which measures the same coherencefunction in a reciprocal configuration, i.e. the same splitter/coupleris used for both input splitting and output recombination. The PS-OCTsystem and calculations for the OCT interferometer is generallydescribed and explained by the inventors in U.S. patent application Ser.No. 11/446,683, and Provisional Application Ser. No. 60/932,546, hereinincorporated by reference.

As shown in FIG. 2, The PS-OCT system has a light source 210 withcascaded fiber optic couplers to subdivide the source light into threeprimary modules (1) the primary OCT interferometer, (2) an auxiliarywavemeter interferometer 260, and (3) an optical trigger generator 262.In one embodiment, the light source 210 is a High Speed Scanning LaserHSL-2000 (Santec) with an instantaneous coherence length of over 10 mm.The swept laser source 210 includes emitted light with a mean frequencyof the output spectrum that varies over time. The mean frequency oflight emitted from the swept source may change continuously over time ata tuning speed that is greater than 100 terahertz per millisecond andrepeatedly with a repetition period. The swept laser source may be anytunable laser source that rapidly tunes a narrowband source through abroad optical bandwidth. The tuning range of the swept source may have atuning range with a center wavelength between approximately 500nanometers and 2000 nm, a tuning width of approximately greater than 1%of the center wavelength, and an instantaneous line width of less thanapproximately 10% of the tuning range. Optionally, the swept lasersource 210 is coupled to an electro-optic polarization modulator tomodulate the polarization state of the source light periodically in timebetween two semi orthogonal polarization states.

As shown in FIG. 2, the auxiliary wavemeter 260 and the optical triggergenerator 262 are for clocking the swept light source in order forproviding an external clock signal to a high speed digitizer 270, asdisclosed in commonly assigned application Ser. No. 60/949,467, filedJul. 12, 2007, herein incorporated by reference. The Uniform FrequencySample Clock signal is repeatedly outputted for each subsequent opticaltrigger that occurs as the laser is sweeping and the optical trigger isgenerated. The optical trigger is generated from the optical triggergenerator 262. The high-speed digitizer card 270 is coupled to theoutput of the OCT interferometer, output of the auxiliary interferometer260, the trigger signal from the trigger generator 262, and thearbitrary waveform generator. The high-speed PCI digitizer card 270 canbe a dual-channel high resolution 16 bit, 125 MS/s waveform for a PCIbus. The external sample clock signal is derived from an auxiliaryoptical wavemeter photoreceiver during a start-up calibration step, andthen repeatedly outputted by the arbitrary waveform generator for eachsubsequent optical trigger signal that occurs as the laser is sweeping.The external clocking system allows for the wavemeter-generated clocksignal to be filtered and processed in software before being outputtedon the arbitrary waveform generator. Thus, the external clock derivedfrom the auxiliary wavemeter is regenerated by the arbitrary waveformgenerator (Gage CompuGen) to allow acquisition of interferometer outputdata directly in wavenumber (k) space.

Coupler 212 splits 90% of the light source power is split into theprimary OCT interferometer and 10% into the coupler 216 for theauxiliary wavemeter 260 and trigger generator 262. A polarizationmodulator may be placed in the source path to modulate the polarizationstate of the light source periodically in time between two“semi-orthogonal” polarization states. The modulation cycle may besynchronized to the wavelength scan or during each A-line scan. Coupler214 then splits the light 90% directed to port 1 of a 3-portpolarization sensitive optical circulator 220 for the sample path and10% of the light is directed to port 1 of a 3-port polarizationsensitive optical circulator 222 for the reference path. Port 2 ofcirculator 220 for the sample path is coupled to a polarizationcontroller 230 and to a sample 240. The polarization controller 230 mayinclude, but is not limited to, a fiber-optic polarization controllerbased on bending-induced birefringence or squeezing. The polarizationcontroller 230 can be used to match the polarization state of thereference arm to that of the sample arm. Alternatively, the polarizationcontroller 230 may be a polarization control circuit. The sample pathcan be coupled to a probe or catheter 242 via a fiber optic rotaryjunction. Examples of a rotating catheter tip for the sample pathinclude, a turbine-type catheter as described in Patent CooperationTreaty application PCT/US04/12773 filed Apr. 23, 2004; or a rotatingoptical catheter tip as described in U.S. patent application Ser. No.11/551,684; or a rotating catheter probe as described in U.S. patentapplication Ser. No. 11/551,684; or an OCT catheter as described inProvisional Application Ser. No. 61/051,340, filed May 7, 2008, eachherein incorporated by reference for the methods, apparatuses andsystems taught therein. The catheter 242 can be located within a subjectto allow light reflection off of subject tissues to obtain opticalmeasurements, medical diagnosis, treatment, and the like.

The coupler 216 also receives from port 3 of optical circulator 222,where port 2 of optical circulator 222 includes a polarizationcontroller 232 and a Variable Delay Line (“VDL”) 246. The VDL 246comprises of an input fiber, a retro-reflecting mirror on a translationstage, and an output fiber. A dial controls the variable length, ordelay, inserted into the optical path. The typical length variance isabout 6 cm, while the typical time delay is about 300 picoseconds.Alternatively, an adjustable phase delay system can be included tomodulate phase, which includes a piezo-operated stage, to provide muchfiner phase control, e.g., in the sub-wavelength range. Incontradistinction, the VDL provides for larger path-length adjustmentswith micron-size adjustment being the smallest increments. Optionally,the VDL may be coupled to an OCT implementation 252 that allows for asingle detection path or receiver, which is generally described in U.S.patent application Ser. No. 12/018,706, incorporated by referenceherein.

In one embodiment, the photoreceiver 250 comprise a detection element,such as an InGaAs photodiode and a transimpedance amplifier, whichconverts the electrical current signal generated by photons absorbed bythe photodetector element into a voltage signal that can be read by thedigitizer. In one embodiment, a polarizing beam splitter divideshorizontal and vertical polarization components returning from thesample and reference paths. Dual photoreceivers measure horizontal andvertical interference fringe intensities versus depth, Γ_(h)(z) andΓ_(v)(z), respectively. Alternatively, spectral interferometrictechniques with polarization sensitivity may be implemented by recordingfour sequential single-channel measurements or simultaneous dual-channelhorizontal and vertical polarization component measurements inconjunction with the well characterized reference path. Typically, somegain amplification is given at this stage or in a following stage, aswell as some filtering for removing noise that is outside of therelevant electrical bandwidth. The gained and filtered voltage signal isdigitized. The OCT interferogram [S(k)] is digitized at 16-bitresolution using a high-speed PCI digitizer board 270 (AlazarTechATS660, Toronto, Canada) coupled to photoreceiver 250 and the primaryOCT signal and auxiliary wavemeter 260 signal. The external clockderived from the wavemeter and regenerated by the arbitrary waveformgenerator (Gage CompuGen) allows acquisition of data directly inwavenumber (k) space. S(k) is converted using the Fast Fourier Transform(FFT) into the pathlength (z) domain. The magnitude of the transformedOCT A-scan [|S(z)|] represents the backscattered magnitude at depth z inthe sample. The digitizer 270 is coupled to a computer processor, whichis a state-of-the-art workstation with a fast multi-core processor, RAIDstriped disk array, and large RAM space.

In one embodiment, if the PS-OCT system 200 is coupled to catheter 242then the sample path of the OCT system can propagate through acalibration system 248 including a plurality of retardation plates onthe distal end of the sample path fiber to have its polarization statetransformed, as shown in FIG. 2. The detected transformation will bedifferent than the expected and actual transformation due to theambiguity caused by the fiber optic. Polarization ambiguity in afiber-based PS-OCT can change dramatically upon movement and bending ofthe fiber cable during catheterization procedures. Using the methoddescribed herein, the comparison of the detected transformation with theexpected transformation of polarization in the system of retardationplates will provide calibration coefficients, such as the Jones matrixof the catheter fiber, to overcome the ambiguity and compensate orcorrect polarization data from back-scattering events happening distalto the calibration retardation plate system. An exemplary catheter forOCT systems is disclosed in common assigned provisional application Ser.No. 60/949,511, filed Jul. 12, 2007, herein incorporated by reference.

The calibration system 248 includes a system of retardation plates withat least a first birefringent material and a second birefringentmaterial. If a PS-OCT approach is used to calibrate, each retardationplate must have sufficient thickness and reflectivity to be visualizedin an OCT image. In one embodiment, each retardation plate can bevisualized concurrently with specimen imaging. The calibrationretardation plate system can be imaged in the same A-scan if scan depthis sufficiently long, or with a separate interferometer (separatereference arm of different path length and separate readout) sharingonly the sample path (catheter) fiber. Light must be focused/collimatedand reflectivity chosen such that signal-to-noise ratio from surfaces ofretardation plates is sufficiently high to avoid noise in calibrationcoefficients but not have detrimental self-interference patterns in thespecimen imaging interferometer. One of the references would have to belooking at a non-focused image.

Calibration may be used to detect absolute axis orientations usingsingle mode fiber base PS-OCT. Calibration requires that some signal becollected from a known element distal to the entire fiber. There areseveral different embodiments for a calibration system in the distal,post-fiber portion of a catheter probe. In one embodiment, separateretardation plates are placed between collimating/focusing elements anda rotating/deflecting prism. The collimating/focusing elements can beGRIN lenses.

In another embodiment, dual-layered birefringent material is used as thecapsule material of the catheter. In another embodiment, the sample beamis split with a partially reflective prism, which allows the transmittedportion to propagate to the calibrating retardation plates. Such anembodiment could be used for Doppler OCT calibration. In anotherembodiment, the sample beam is split with a dichroicwavelength-dependent prism and a separate light source is used tocalibrate the fiber independently of the imaging beam. Such anembodiment allows the calibrating signal to be completely independent ofthe imaging signal. The calibration will be for a different wavelengththan the imaging signal wavelength and Polarization Mode Dispersion(“PMD”) will be adjusted and considered accordingly. In anotherembodiment, a separate interferometer is coupled to the sample path withthe retardation plates, in order to separately image the retardationplate system. The separate interferometer includes a separate referencearm of different optical path length and separate readout.

Birefringence and Retardation

Form-birefringence is an optical property exhibited by media containingordered arrays of anisotropic light scatterers which are smaller thanthe wavelength of incident light. Form-birefringence arises inbiological structures when cylindrical fibers with diameters on thissize scale are regularly oriented in a surrounding medium with differentrefractive index. The electric field of incident light oscillatingperpendicular to the fibers (Ε_(⊥)) induces surface charges that createan induced field (Ε_(o)) within the fiber, as shown in FIG. 6. Theinduced field (Ε_(o)) anisotropically modifies forward scattered lightso that phase and amplitude of Ε_(⊥) is altered relative to the electricfield component polarized parallel to the fibers (Ε_(∥)). The electricfield of incident light which is polarized perpendicular to the fiberaxis (Ε_(⊥)) produces a surface charge density with an induced field(Ε_(o)). This changes the dielectric susceptibility and gives higherrefractive index (n_(s)) relative to that experienced by light polarizedparallel to the fiber axis (Ε_(∥)). Form-biattenuance (Δ_(χ)) causesanisotropic attenuation of amplitude between Ε_(⊥) and Ε_(∥). Manyfibrillar tissue structures are optically anisotropic; however, valuesof Δn vary considerably among species and tissue type.

The incremental phase retardation (δ_(i)) incurred by the perpendicularcomponent (Ε_(⊥)) results in slower light transmission and largerrefractive index (n_(s)) than that experienced by light polarizedparallel to the fiber axis (Ε_(∥)) with refractive index n_(f).Incremental phase retardations (δ_(i)) accumulate through fibrousstructures and the composite retardation (δ) between componentspolarized parallel (Ε_(∥)) and perpendicular (Ε_(⊥)) to the fibers afterpropagating a distance Δz is:

$\begin{matrix}{\delta = \frac{360\; \Delta \; n\; \Delta \; z}{\lambda_{o}}} & (15.1)\end{matrix}$

where δ is given in degrees. Similarly, the compositerelative-attenuation (∈) between components polarized parallel (Ε_(∥))and perpendicular (Ε_(⊥)) to the fibers after propagating a distance Δzis:

$\begin{matrix}{ɛ = {{\frac{{360 \cdot \Delta}\; \chi}{\lambda_{o}} \cdot \Delta}\; z}} & (15.2)\end{matrix}$

where ∈ is given in degrees.

Polarimetric Signal to Noise Ratio

Polarimetric speckle noise is one noise source impeding accuratedetermination of polarimetric properties of the sample under test. Incontrast to intensity speckle noise, which is common to bothpolarization channels and only degrades I(z), polarimetric speckle noiseis different for horizontal and vertical polarization channels anddegrades depth resolved polarization data (“S(z)”). Intensity specklenoise is removed in part from polarization data by normalization ofStokes vectors.

First order statistics of the Stokes vector of scattered light for thecase when horizontal and vertical fields are uncorrelated show that theprobability density for the intensity is a sum of two orthogonal specklefields (i.e. horizontal and vertical) and the Stokes parameters areLaplace variants. In some circumstances, speckle statistics of theStokes vector for partially polarized light can be derived assumingGaussian correlated field amplitudes. The statistics of polarimetricspeckle noise likely depend on the tissue under investigation andpossibly configuration of the sample path optics (e.g., numericalaperture of focusing lens, distal optics, and the like).

To quantitatively characterize the ability of the PS-OCT configurationto extract model P(z) from noisy S(z) a polarimetric signal-to-noiseratio (“PSNR”) is introduced:

$\begin{matrix}{{PSNR} = {\frac{l_{arc}}{\sigma_{speckle}} = \frac{2\; \delta \; {\sin (\gamma)}}{\sigma_{speckle}}}} & (15.3)\end{matrix}$

where l_(arc) is arc length of the noise-free model polarization arc[P(z)] associated with measured S(z). Standard deviation of polarimetricspeckle noise (“σ_(speckle)”) is a statistical measure of thepoint-by-point angular variation on the Poincaré sphere between detectedS(z) and model P(z):

$\begin{matrix}{\sigma_{speckle} = \left( {\frac{1}{J}{\sum\limits_{j}\left( {\cos^{- 1}\left( {{S(z)} \cdot {P(z)}} \right)} \right)^{2}}} \right)^{1/2}} & (16)\end{matrix}$

where J is the total number of depth-resolved sample points within thespecimen. By averaging an ensemble of N_(A) uncorrelated speckle fields,σ_(speckle) is reduced and PSNR is increased.

Exemplary Algorithm to Determine Retardation and Birefringence

The analysis for determining retardation from S(z) recorded by thePS-OCT configurations is for a region of sample depths with homogeneouspolarimetric properties. If the sample is heterogeneous in depth, thenretardation by the PS-OCT configurations for each range of depths wherethe sample polarimetric properties are homogenous is completed. In oneembodiment, determining retardation from S(z) recorded with the PS-OCTconfigurations comprises estimating the three model parameters whichmathematically specify the noise-free model polarization arc [P(z)]: (1)angle of arc rotation, which is equal to the double-pass retardation(2δ); (2) rotation axis (A) and (3) the arc's initial point, whichrepresents the polarization at the specimen's front surface [P(0)]. Anonlinear fitting algorithm that takes S(z) as input and estimates modelparameters has been developed. Implementation of the nonlinear fittingalgorithm to estimate (2δ), A, and P(0) comprises formulation of aresidual function (R_(o)) which specifies goodness of fit between S(z)and P(z):

$\begin{matrix}{R_{o} = {\sum\limits_{j}{{{S(z)} - {P\left( {{z;{2\; \delta}},A,{P(0)}} \right)}}}^{2}}} & (17)\end{matrix}$

R_(o) measures cumulative squared deviation between noisy S(z) andnoise-free P(z). Model parameters are estimated by minimizing R_(o)using a Levenberg-Marquardt algorithm and represent the best estimate ofP(z).

Because PSNR increases with separation-angle (γ, Eq. (15.3)), thepolarization at the specimen's front surface [P(0)] which gives γ=90°provides the optimal incident polarization state for most accuratedetermination of δ. Because birefringence of preceding layers (e.g.single-mode optical fiber, anterior segment of the eye) is generallyunknown, one is unable to select a priori a P(0) that provides a maximumseparation-angle γ=90°. To resolve the problem of preceding unknownbirefringent layers and estimate 2δ and A accurately, a multi-statenonlinear algorithm that uses M incident polarization states uniformlydistributed on a great circle of the Poincaré sphere is employed.Utilizing multiple incident polarization states gives M distinctseparation-angles (γ_(m)) distributed within the interval [0°, 90°]insuring that γ_(m)=90° for some states. By using a multi-stateapproach, variance in estimated (2δ) due to either uncertainty in A orlow PSNR is minimized.

Implementation of the multi-state nonlinear algorithm to determine δrequires formulation of a multi-state residual function. A multi-stateresidual function (R_(M)) that is the algebraic sum of R_(o) (Eq. (17))over the M incident polarization states is:

$\begin{matrix}{R_{M} = {\sum\limits_{m = 1}^{M}{R_{o}\left( {{{S_{m}(z)};\delta},A,{P_{m}(0)}} \right)}}} & (18)\end{matrix}$

R_(M) gives the composite squared deviation between M sets ofdepth-resolved polarization data [S_(m)(z)] and corresponding Mnoise-free model polarization arcs [P_(m)(z)]. Model parameters [2δ, A,and P_(m)(0)] are estimated by minimizing R_(M) using aLevenberg-Marquardt algorithm and represent the best estimates ofP_(m)(z) arcs.

The ability of the multi-state nonlinear algorithm to determine modelparameters is verified on simulated noisy depth-resolved polarizationdata. The multi-state approach comprises all M noise-free modelpolarization arcs [P_(m)(z)] that rotate around the same rotation axis Aby the same angle (2δ) regardless of P_(m)(0), l_(arc,m), or γ_(m). Theuncertainty in any single P_(m)(z) arc is offset through constraintsplaced upon the other M−1 arcs by the multi-state residual function. Inaddition, the multi-state nonlinear algorithm comprises a singleestimate of unknown parameters using all depth-resolved data points inthe scan, allowing the consideration of more than two points at a time[S(0) and S(Δz)] and the incorporation of S(z) arc curvature.

Birefringence in tissue is predominantly the form type and results froman anisotropic distribution of refractive index from ordered fibrillarstructures. For high sensitivity quantification of birefringence withthe PS-OCT configurations, a nonlinear fitting of normalized Stokesvectors from multiple incident polarization states provides accuratedetermination of retardation in thin, weakly birefringent tissuespecimens such as a turbid birefringent film. Disordering of fibrillartissue structure in response to a pathological condition will likelymodify the birefringence; therefore, the highly sensitive PS-OCTconfiguration detects changes in birefringence, monitors thepathological conditions which alter fibrillar tissue structure,fibrillar structures corresponding to pathological conditions such asfibrous caps (fibrillar structures can correspond to pathologicalconditions such as fibrous caps), and diagnoses other clinicalconditions.

Neurotubule fibrils in unmyelinated axons contribute to Retinal NerveFiber Layer (“RNFL”) form birefringence. Highly sensitive determinationof tissue retardation provides a measure of the number of fibrils(N_(t)), and birefringence may provide a measure of fibril density(ρ_(t)) within the volume sampled by the PS-OCT sample beam. The PS-OCTconfiguration can quantify the number of RNFL neurotubules during theprogression of glaucoma, localize collagen denaturation in the skin ofburn victims, and aid in the diagnosis of other pathologies or traumasthat affect the fibrous structure of form birefringent tissue.

When polarized light propagates through the birefringent RNFL, theeigenpolarization state oriented perpendicular to the neurotubulestravels slower and phase is delayed relative to the paralleleigenpolarization component, resulting in a transformation inpolarization state. Each fibril (e.g. microtubule, collagen filament,actin-myosin complex) acts as a nanoretarder on incident polarized lightand introduces a phase delay between eigen polarizations. Incrementalphase delay δ_(inc)=0.0046° is introduced by individual neurotubules atλ_(o)=546 nm.

Light that propagates to the specimen's rear surface acquires anaccumulated retardation from the nanoretarder fibrils:

$\begin{matrix}{\delta = {\frac{360\; \Delta \; n\; \Delta \; z}{\lambda_{o}} = \frac{360\; f\; \Delta \; n_{t}\Delta \; z}{\lambda_{o}}}} & (19)\end{matrix}$

where f is the local volume fraction of fibrils in the sampled specimenvolume, λ_(o) is the free-space wavelength of incident light, and Δn_(t)is the specific birefringence of the fibril (sometimes referred to asthe birefringence-per-volume fraction), Δz is the thickness from thefront surface to the rear surface. The local volume fraction (r) offibrils within the sampled specimen volume (V) may be written as:

$\begin{matrix}{f = \frac{N_{t}v_{o}}{V}} & (20)\end{matrix}$

where N_(t) is the number of fibrils in V and v_(o) is the volumeoccupied by a single fibril within V. The sampled specimen volume V, maybe approximated by a cylinder of light defined by the beam waist radius(w_(o)) and specimen thickness (Δz):

V=πw _(o) ² _(Δz)  (21)

where A_(o) is the cross-sectional area of one fibril. For a givenw_(o), the determination of specimen thickness and retardation providesa measure of the number (N_(t)) and density (ρ_(t)) of fibrils in thesampled specimen volume:

$\begin{matrix}{{N_{t} = {\frac{\pi \; \lambda_{o}w_{o}}{1440\; \Delta \; n_{t}A_{o}}\delta}},} & (22) \\{\rho_{t} = {{\frac{\pi \; \lambda_{o}}{1440\; \Delta \; n_{t}A_{o}w_{o}}\left( \frac{\delta}{\Delta \; z} \right)} = {\frac{\pi}{4\; \Delta \; n_{t}A_{o}w_{o}}\Delta \; {n.}}}} & (23)\end{matrix}$

The number of fibrils in the sampled specimen volume scales with 6. Thedensity of fibrils scales with Δn.

The values of the scaling parameters in Eqs. (23) for neurotubules inthe RNFL by assuming a beam waist radius (w_(o)=10 mm) and a free-spacewavelength (λ_(o)=0.83 μm) and by using known values for theneurotubule-specific birefringence (Δn_(t)=0.025) and cross-sectionalarea [A₀=π(12 nm)²=450 nm²]. Δδ_(RNFL) is used to estimate the number ofneurotubules in the nasal (N_(t)≈17×10³) and inferior (Nt≈z133×10³)regions. Similarly, Δn_(RNFL) shows the neurotubule density isconsiderably lower in the nasal region (ρ_(t)≈1.1 μm⁻³) than in theinferior region (ρ_(t)≈2.5 μm⁻³).

Form Biattenuance

In the eigenpolarization coordinate frame, the polarization-transformingproperties of a non-depolarizing, homogeneous optical medium such asanisotropic fibrous tissue are described by the Jones matrix

$\begin{matrix}{J = {\begin{bmatrix}{\exp \left( {\left( {{\Delta \; \chi} + {\; \Delta \; n}} \right){\pi\Delta}\; {z/\lambda_{0}}} \right)} & 0 \\0 & {\exp \left( {\left( {{{- \Delta}\; \chi} - {\; \Delta \; n}} \right){\pi\Delta}\; {z/\lambda_{0}}} \right)}\end{bmatrix} = {\quad\begin{bmatrix}{{\xi_{1}}{\exp \left( {\; {\arg \left( \xi_{1} \right)}} \right)}} & 0 \\0 & {{\xi_{2}}{\exp \left( {\; {\arg \left( \xi_{2} \right)}} \right)}}\end{bmatrix}}}} & (24)\end{matrix}$

where ξ₁ and ξ₂ are the complex eigenvalues representing changes inamplitude and phase for orthogonal eigenpolarization states withfree-space wavelength λ_(o) propagating a distance Δz through themedium. Attenuation common to both eigenpolarizations does not affectthe light polarization state and is neglected here.

The phase retardation (δ, expressed in radians) betweeneigenpolarization states after propagation through the medium is thedifference between the arguments of the eigenvalues, δ=arg(ξ₁)−arg(ξ₂),which allows simplification of the Jones matrix to

$\begin{matrix}{J = {\begin{bmatrix}{{\xi_{1}}{\exp \left( {\; {\delta/2}} \right)}} & 0 \\0 & \left. {{\xi_{2}}{\exp \left( {{\delta}/2} \right)}} \right)\end{bmatrix}.}} & (25)\end{matrix}$

The polarimetric parameter diattenuation (D) is given quantitatively by:

$\begin{matrix}{{D = {\frac{{T_{1} - T_{2}}}{T_{1} + T_{2}} = \frac{{}\xi_{1}{^{2} - }\xi_{2}{^{2}}}{{\xi_{1}}^{2} + {\xi_{2}}^{2}}}}{{0 \leq D \leq 1},}} & (26)\end{matrix}$

where T₁ and T₂ are the intensity transmittances for the two orthogonaleigenpolarizations and the attenuation can be a consequence of eitheranisotropic absorption or anisotropic scattering of light out of thedetected field.

Birefringence (Δn) is the phenomenon responsible for phase retardation(δ) of light propagating a distance Δz in an anisotropic element and isgiven by:

$\begin{matrix}{{{\Delta \; n} = {{\frac{\lambda_{0}}{2\; \pi}\frac{\delta}{\Delta \; z}} = {n_{s} - n_{f}}}},} & (27)\end{matrix}$

where n_(s) and n_(f) mare the real-valued refractive indicesexperienced by the slow and fast eigenpolarizations, respectively.Form-birefringence (Δn) is proportional to and given experimentally bythe phase retardation-per-unit-depth (δ/Δz).

Dichroism describes the phenomenon of diattenuation in ananisotropically absorbing element (such as that exhibited by a sheetpolarizer), and the term is also used to describe differentialtransmission or reflection between spectral components (such as thatexhibited by a dichroic beam splitter), leading to confusion if taken inthe incorrect context. Neither dichroism nor diattenuation norpolarization dependent loss (“PDL”) can be expressed on a per-unit-depthbasis and are thus unsuitable quantities for depth-resolved polarimetryin scattering media. Attenuance has come to describe the loss oftransmittance by either absorption or scattering; biattenuance is thedifferential loss of transmittance between two eigenpolarization statesby either absorption (dichroism) or scattering. Form-biattenuance is anexperimentally and theoretically relevant term that can be expressed ona per-unit-depth basis. Numerically, biattenuance (“Δ_(χ)”) is given byEquation (28):

Δ_(χ)=χ_(s)−χ_(f),  (28)

where χ_(s) and χ_(f) are attenuation coefficients of the slow and fasteigenpolarizations. For absorbing (dichroic) media, χ_(s) and χ_(f) aresimply imaginary-valued refractive indices.

The phase retardation (δ) and thickness (Δz) of an element are linearlyrelated by its birefringence (Δn). However, the relationship between anelement's diattenuation [D, Eq. (26)] and thickness (Δz) is nonlinear.This nonlinear relationship complicates expression of an element'sform-biattenuance: one cannot generally and without approximation referto a diattenuation-per-unit-depth as one can refer to form-birefringenceas a phase retardation-per-unit-depth. For example, if optical element Ahas thickness Δ_(ZA)=1 mm, diattenuation D_(A)=0.4, and phaseretardation δ_(A)=π/4 radians and element B is made of the same materialbut has twice the thickness Δ_(ZB)=2 mm, element B will have twice thephase retardation δ_(B)=2δ_(A)=π/2 radians but will not have twice thediattenuation D_(B)=0.69≠2D_(A).

For depth-resolved polarimetry in scattering media (i.e. PS-OCT),expression of an element's form-biattenuance on a per-unit-depth basisis desirable theoretically and experimentally. The relative attenuation(∈) experienced by light propagating to a depth Δz in an anisotropicelement is defined as:

$\begin{matrix}{{ɛ = {\frac{2\; \pi}{\lambda_{0}}\Delta \; z\; \Delta \; \chi}},} & (29)\end{matrix}$

and form-biattenuance (Δ_(χ)) can now be meaningfully expressed on arelative attenuation-per-unit-depth basis (∈/Δz). Relative-attenuation(∈) is the complimentary term to phase retardation [δ, Eq. (27)], justas biattenuance (Δz) is the complementary term to birefringence (Δn).

The Jones matrix of the anisotropic medium from Eqs. (24) and (25)becomes

$\begin{matrix}{{J = \begin{bmatrix}{\exp \left( \frac{ɛ + {\; \delta}}{2} \right)} & 0 \\0 & {\exp \left( {- \frac{ɛ - {\delta}}{2}} \right)}\end{bmatrix}},} & (30)\end{matrix}$

and the “anisotropic damping” effect of the relative-attenuation (∈)becomes apparent. Diattenuation (D) is related to relative-attenuation(∈) by:

$\begin{matrix}{D = {\frac{{^{ɛ} - ^{- ɛ}}}{^{ɛ} + ^{- ɛ}} = {{\tanh (ɛ)}.}}} & (31)\end{matrix}$

For small relative-attenuation, a small-angle approximation is valid andD≈c.

Dual attenuation coefficients (μ_(ax) and μ_(ay)) to represent Beer'slaw attenuation for each eigenpolarization can be related todiattenuation (D) using Eq. (31) where relative-attenuation (∈) isrelated to dual attenuation coefficients by ∈=|μ_(ax)−μ_(ay)|Δz/2. Phaseretardation (δ) is in the argument of an exponential [Eq. (30)] andtherefore has units of radians, but is also commonly expressed in unitsof degrees (180·δ/π), fractions of waves (δ/2π), or length (λ₀δ/2π).Similarly, relative attenuation (∈) is in the argument of an exponential[Eq. (30)] and has units of radians. The expression ofrelative-attenuation in units of radians (or degrees, fractions ofwaves, or length) is less intuitive than for phase retardation.

Exemplary Signal Conditioning

In one embodiment, detected photocurrents representing horizontal andvertical polarimetric fringe signals (Γ_(h)(z) and Γ_(v)(z)) arepre-amplified, bandpass filtered, and digitized. Coherent demodulationof Γ_(h)(z) and Γ_(v)(z) yields signals proportional to the horizontaland vertical electric field amplitudes [E_(h)(z) and E_(v)(z)] andrelative phase [Δφ(z)] of light backscattered from the specimen at eachdepth z within the A-scan. An ensemble (N_(A)) of A-scans representinguncorrelated or weakly correlated speckle fields are acquired on a gridwithin a small square region (50 μm×50 μm) at each location of intereston the specimen. Acquisition of an ensemble of N_(A) A-scans at eachlocation is repeated for M incident polarization states distributed inuniform increments on a great circle on the Poincaré sphere by M phaseshifts (δ_(LCVR,m)) of a polarization control element (e.g., LiquidCrystal Variable Retarder, LCVR). For each M, the calibrated LCVR phaseshift (δ_(LCVR,m)) is subtracted from the demodulated relative phase[Δφ_(m)(z)] to compensate for the light's return propagation through theLCVR. This yields M sets of horizontal and vertical electric fieldamplitudes [E_(h,m)(z) and E_(v,m)(z)] and compensated relative phase[Δφ_(c,m)(z)]. Non-normalized Stokes vectors are calculated fromE_(h,m)(z), E_(v,m)(z), and Δφ_(c,m)(z) for each of N_(A) A-scans in theensemble and for each M. Ensemble averaging over N_(A) at each depth z(denoted by < >_(N) _(A) ) reduces σ_(speckle) by a factor ofapproximately N_(A) ^(1/2) and then normalization yields M sets ofdepth-resolved polarization data [S_(m)(z)] for each location,

$\begin{matrix}{{S_{m}(z)} = {\begin{pmatrix}{Q(z)} \\{U(z)} \\{V(z)}\end{pmatrix} = \frac{\begin{pmatrix}{\langle{{E_{h,m}(z)}^{2} - {E_{v,m}(z)}^{2}}\rangle}_{N_{A}} \\{\langle{2\; {E_{h,m}(z)}{E_{v,m}(z)}{\cos \left\lbrack {\Delta \; {\varphi_{c,m}(z)}} \right\rbrack}}\rangle}_{N_{A}} \\{\langle{2\; {E_{h,m}(z)}{E_{v,m}(z)}{\sin \left\lbrack {{\Delta\varphi}_{c,m}(z)} \right\rbrack}}\rangle}_{N_{A}}\end{pmatrix}}{{\langle{{E_{h,m}(z)}^{2} + {E_{v,m}(z)}^{2}}\rangle}_{N_{A}}}}} & (32)\end{matrix}$

When Stokes vectors are first normalized and then ensemble-averaged overN_(A), the resulting Stokes vectors [W_(m)(z)] have magnitude[0≦|W_(m)(z)|=W_(m)(z)≦1] which is directly related to the extent of thedistribution of pre-averaged normalized Stokes vectors on the Poincarésphere within the ensemble at each depth z,

$\begin{matrix}{{W_{m}(z)} = {{\langle\frac{\begin{pmatrix}{{E_{h,m}(z)}^{2} - {E_{v,m}(z)}^{2}} \\{2\; {E_{h,m}(z)}{E_{v,m}(z)}{\cos \left\lbrack {\Delta \; {\varphi_{c,m}(z)}} \right\rbrack}} \\{2\; {E_{h,m}(z)}{E_{v,m}(z)}{\sin \left\lbrack {{\Delta\varphi}_{c,m}(z)} \right\rbrack}}\end{pmatrix}}{{E_{h,m}(z)}^{2} + {E_{v,m}(z)}^{2}}\rangle}_{N_{A}}.}} & (33)\end{matrix}$

W_(m)(z) is used as a scalar weighting factor in the multistatenonlinear algorithm to estimate phase retardation (δ) andrelative-attenuation (δ).

Exemplary Multistate Nonlinear Algorithm to Determine Form-Biattenuance

In one embodiment, high sensitivity quantification of form-biattenuance(Δ_(χ)) is accomplished using a nonlinear fitting algorithm based on theapproach for determining form-birefringence (Δn) with the PS-OCTconfigurations. A modified multistate residual function (R_(m)) may beimplemented which gives the composite squared deviation between M setsof depth-resolved polarization data [S_(m)(z)] and corresponding Mnoise-free model polarization arcs [P_(m)(z)] weighted by W_(m)(z),

$\begin{matrix}{R_{M} = {\sum\limits_{m = 1}^{M}{R_{o}\left\lbrack {{S_{m}\left( z_{j} \right)},{{W_{m}\left( z_{j} \right)};{2\; ɛ}},{2\; \delta},\hat{\beta},{P_{m}(0)}} \right\rbrack}}} & (34)\end{matrix}$

where R_(o) is the weighted single-state residual function,

$\begin{matrix}{{R_{o} = {\sum\limits_{j = 1}^{J}\left\{ {{W_{m}\left( z_{j} \right)}\left\lbrack {{S_{m}\left( z_{j} \right)} - {P\left\lbrack {{z_{j};{2\; ɛ}},{2\; \delta},\hat{\beta},_{m}{P(0)}} \right\rbrack}} \right\rbrack} \right\}^{2}}},} & (35)\end{matrix}$

and the subscript “j” is used to denote the discrete nature of sampleddata versus depth (z). Model parameters [2∈, 2δ, {circumflex over (β)},and P_(m)(0)] are estimated by minimizing Rousing a Levenberg-Marquardtalgorithm and represent the best estimate of P_(m)(z). At increasedpenetration depths (lower electrical signal-to-noise ratio) or largeinitial separation-angles [γ_(m)(0)], W_(m)(z) decreases and S_(m)(z)are given less weight. Δ_(χ) and Δn are calculated using Eqs. (27) and(29) from estimates of ∈ and δ provided by the multistate nonlinearalgorithm. Δz is measured by subtracting the front and rear specimenboundaries in the OCT intensity image and dividing by the bulkrefractive index (n=1.4).

Uncertainty in estimates of any single P_(m)(z) arc is offset throughconstraints placed upon the other M−1 arcs by the modified residualfunction [Eq. (34)]. All M noise-free model polarization arcs [P_(m)(z)]must collapse toward the same eigen-axis ({circumflex over (β)}) at thesame rate (2∈) and must rotate around {circumflex over (β)} by the sameangle (2δ) regardless of the incident polarization state. Discriminationbetween arc movements on the Poincaré sphere due to either Δn or Δ_(χ)is accomplished by restricting contributions from each into orthogonalplanes.

Model for Form-Biattenuance and Form-Birefringence

The phenomenon of form-biattenuance and a model predicting the relativecontribution of Δn and Δ_(χ) to transformations in polarization state oflight propagating in anisotropic media is shown in FIG. 7. The model maybe used as examples of tissues with alternating anisotropic media andisotropic layers. Other models are possible that would generally beconsidered to explain polarimetric properties of tissues.

Optical Axis Orientation

Optic axis orientation (θ) provides the direction of constituent fibersrelative to a fixed reference direction (i.e., horizontal in thelaboratory frame). A method for measuring depth-resolved optic axisorientation [θ(z)] deep within multiple layered tissues uses the PS-OCT,as described previously.

Collagen organization in cartilage and intervertebral disc cartilage maybe used as a model tissue on which to demonstrate the depth-resolvedpolarimetric imaging ability of PS-OCT. As shown in FIG. 8,intervertebral discs are located between spinal vertebrae and consist ofthe annulus fibrous (“AF”), enclosing an inner gel-like nucleus pulposis(“NP”). Annulus fibrous is composed of axially concentric rings (i.e.lamellae) of dense type I collagen fibers (fibrocartilage), theorientation of which is consistent within a single lamella butapproximately perpendicular to fibers in neighboring lamellae, forming alattice-like pattern. Regular orientation of collagen fibers within asingle lamella is responsible for form-birefringence [Δn(z)], andalternating fiber directions between successive lamellae correspond toalternation of optic axis orientation [θ(z)] within the annulus fibrous.

Multiple layered fibrous tissue such as the annulus fibrous is modeledas a stack of K linearly anisotropic, homogeneous elements, each witharbitrary phase retardation (δ_(k)), relative-attenuation (∈_(k)), opticaxis orientation (θ_(k)), and corresponding kth Jones matrix[J_(s(k))(δ_(k),∈_(k),θ_(k))]. Incident polarized light (E_(in))propagating to the rear of the kth intermediate element and back out indouble-pass (E_(dp) _(—) _(out(k))) is represented by:

E _(dp) _(out) _(out(k)) =J _(s(1)) ^(T) J _(s(2)) ^(T) . . . J_(s(k-1)) ^(T) J _(s(k)) ^(T) J _(s(k)) J _(s(k-1)) . . . J _(s(2)) J_(s(1)) E _(in).  (41)

For the most superficial layer (k=1), Eq. (41) becomes E_(dp) _(—)_(out(1))=J_(s(1) T)J_(s(1))E_(in), and J_(s(1))(δ₁,∈₁,θ₁) can berecovered using matrix algebra. Likewise, δ₁, ∈₁, and θ₁ can be foundusing a nonlinear fit to the trajectory between S_(in) and S_(dp) _(—)_(out(1)) on the Poincaré sphere and Eq. (42):

θ=sgn(β_(u))cos⁻¹({circumflex over (β)}·{circumflex over (q)})/2  (42)

where {circumflex over (q)} is the unit-vector defining the Q axis ofthe three-dimensional Cartesian coordinate system containing thePoincaré sphere and β_(u) is the U component of {circumflex over (β)}.

For the next layer (k=2), Eq. (41) becomes E_(dp) _(—)_(out(2))=J_(s(1)T)J_(s(2) T) J_(s(2))J₍₁₎E_(in). Matrix algebra andknowledge of J_(s(1)) allows recovery of J_(s(2))(δ₂,∈₂,θ₂). Likewise,δ₂, ∈₂, and θ₂ can be found using a nonlinear fit to the trajectorybetween S_(dp) _(—) _(out(1)) and S_(dp) _(—) _(out(2)) aftercompensation of anisotropy in the superficial layer (reverse rotation by−δ₁ and reverse collapse by −∈₁ with respect to {circumflex over (β)}₁).This process is repeated for successively deeper layers in the stack todetermine δ_(k), ∈_(k), and θ_(k) for all k layers.

In PS-OCT imaging, the polarization state detected after double-pass tothe rear of the kth intermediate element [E_(dp) _(—) _(out(k)), Eq.(41)] is also transformed by optics in the instrument (e.g.,beamsplitter, optical fiber, polarization modulator, retroreflector),adding complexity to the optic axis orientation analysis. With inclusionof a Jones matrix (J_(c)) which encompasses instrumentaltransformations, Eq. (41) becomes:

E _(dp) _(out) _(out(k)) =J _(c) ^(T) J _(s(1)) ^(T) . . . J _(s(k-1))^(T) J _(s(k)) ^(T) J _(s(k)) J _(s(k-1)) . . . J _(s(1)) J _(c) E_(in).  (43)

For a single-mode-fiber-based PS-OCT configuration, J_(c) representsunstable phase retardation between arbitrary elliptical eigenvectors. Inthis case, eigenvectors of Jones matrices in Eq. (43) vary in an unknownfashion and measurement of the anatomical fiber direction with respectto the laboratory frame is distorted by the optical fiber birefringence.The calibration system 248 may allow fiber-based PS-OCT configurationsto overcome distortion in the optical fiber. The PS-OCT instrument hasstable J_(c) with linear eigenvectors in the laboratory frame; thereforeJ_(c) reduces to simple phase retardation (δ_(c), due to thebeamsplitter and retroreflector) between horizontal and verticalinterference fringes. In one embodiment, the PS-OCT configurationincorporates a liquid crystal variable retarder (“LCVR”) to modulate thelaunched polarization state incident on the specimen by applying avoltage-controlled phase retardation (δ_(LCVR)). The optic axis of theLCVR is horizontal, thus the total systematic phase retardation(δ_(LCVR)+δ_(c)) can be compensated by subtraction of δ_(LCVR)+δ_(c)from the relative phase of the detected horizontal and verticalinterference fringe signals, allowing unambiguous and undistortedmeasurement of the anatomical fiber direction (θ_(k)) absolutelyreferenced to the laboratory frame.

Depth-Resolved Identification

Transformations in the depth-resolved polarization state of lightbackscattered from linearly anisotropic media such as fibrous tissue canbe represented as depth-resolved normalized Stokes vector (S(z)) arcs onthe Poincaré sphere. The trajectory of S(z) arcs in the presence of Δnand Δ_(χ) is governed by a vector differential equation, as by a vectordifferential equation. Briefly, S(z) arcs rotate in a circulartrajectory around an eigenaxis ({circumflex over (β)}) by an angle equalto the double-pass phase retardation (2δ) of the specimen. Phaseretardation (δ, radians) is related to tissue birefringence (Δn),wavelength (λ₀) and specimen thickness (Δz) by δ=2πΔnΔz/λ₀. S(z) arcsalso collapse towards {circumflex over (β)} by an angle related to thedouble-pass relative attenuation (∈, radians), which is proportional totissue biattenuance (Δ_(χ)), wavelength and specimen thickness by∈=2πΔ_(χ)Δz/λ₀. The combined effect, a spiraling collapse of S(z)towards {circumflex over (β)}, occurs for tissues exhibiting both Δn andΔ_(χ).

Eigenaxis ({circumflex over (β)}) is directly related to the fiberorientation (θ) given with respect to the horizontal byθ=sgn({circumflex over (β)}_(u) cos⁻¹({circumflex over (β)}·{circumflexover (q)}/2), where {circumflex over (q)} is the unit vector definingthe Q-axis of the three-dimensional Cartesian coordinate systemcontaining the Poincaré sphere and {circumflex over (β)}_(u) is the Ucomponent of {circumflex over (β)}. When θ is constant and biattenuanceis negligible (Δ_(χ)<<Δn), the curvature (κ(z)) of the S(z) arc isnearly constant and is approximated by:

$\begin{matrix}{{\kappa (z)} \approx \frac{1}{\cos^{- 1}\left\lbrack {{S(z)} \cdot \hat{\beta}} \right\rbrack}} & (44)\end{matrix}$

where depth-resolved separation-angle γ(z)=cos⁻¹[S(z)·{circumflex over(β)}]. The unit tangent vector [{circumflex over (T)}(z)] of S(z) isgiven by:

$\begin{matrix}{{\hat{T} = \frac{{S(z)}}{l_{arc}}},} & (45)\end{matrix}$

where l_(arc) is the arc length of S(z) on the Poincaré sphere. However,abrupt changes in fiber orientation [θ(z)] versus specimen depth (e.g.in annulus fibrous) produce corresponding changes in both {circumflexover (β)} and in the trajectory of S(z). Discontinuities in the unittangent vector [T̂(z)] give rise to instances of infinite or very largecurvature [κ(z)] for continuous z. For numeric calculation usingdiscrete sampled data (z_(j)=0, 1, 2, . . . ) the unit tangent vectoris:

$\begin{matrix}{{\hat{T}\left( z_{j} \right)} = \frac{{S\left( z_{j} \right)} - {S\left( z_{j - 1} \right)}}{{{S\left( z_{j\;} \right)} - {S\left( z_{j - 1} \right)}}}} & (46)\end{matrix}$

and curvature is:

$\begin{matrix}{{\kappa \left( z_{j} \right)} = {{\frac{{\hat{T}\left( z_{j} \right)} - {\hat{T}\left( z_{j - 1} \right)}}{{{S\left( z_{j} \right)} - {S\left( z_{j - 1} \right)}}}}.}} & (47)\end{matrix}$

FIG. 9A shows simulated depth-resolved polarization data [S(z_(j))] andFIG. 9B shows calculated curvature [κ(z_(j))] for a three-layerbirefringent specimen with constant Δn and three fiber orientationsθ=−10°, 95°, and −5°.

Exemplary Uses of Depth-Resolved Birefringence, Depth-ResolvedBiattenuance, Depth-Resolved Retardation, and Depth-Resolved OpticalAxis

Aneurism vulnerability may be assessed with the PS-OCT configurationsdescribed above. The likelihood of an aneurism rupturing is related tothe mechanical properties of collagen in the arterial walls. If collagenfibers are oriented regularly with the artery longitude, then there isreduced mechanical strength in the perpendicular (circumferential)direction. If aneurisms that contain a more random orientation of fibers(and thus distribute strength in both longitudinal and circumferentialdirections) are less likely to rupture, then the PS-OCT configurationsmay assess the risk or vulnerability of aneurysms' to rupture. In oneembodiment, fiber-based PS-OCT configuration is capable of estimatingabsolute collagen orientation when a known polarization reference isfixed to the distal scanning end. This could be accomplished by using acapsule made out of a known birefringent material as the reference,which is indicated above with a birefringent material in the capsulematerial of the catheter.

For Alzheimer's disease (“AD”), the detection of neurofibrilary tanglesand amyloid plaques using the PS-OCT configuration may be applied fordiagnostic purposes. Cerebral amyloid pathologies exhibit linearbirefringence and dichroism, which may be detected by the PS-OCTconfigurations. In amyloid angiopathy, deposition of collagen fibrils inthe walls of capillaries and veins results in narrowed lumina and evenocclusion has been observed in patients with AD. Collagen XVIIIaccumulates in all types of cerebral blood vessels including arteries,arterioles, capillaries, venules, and veins in patients with AD.Collagen XVIII is associated with amyloid deposition in blood vesselwalls and may be involved in the pathogenesis of AD. The mechanismsleading to the reduced blood flow may be found in the retina and arerelated to those that produce the cerebral blood flow abnormalities inAD. Narrowing of the retinal venous diameter may be related to anincreased venous wall thickness due to collagen deposition, as found incerebral veins. The PS-OCT configurations may assess suchcharacteristics in the characterization of AD.

Also, RNFL thickness measurements using the PS-OCT configurations areuseful in identifying the early changes associated with glaucomatousoptic neuropathy (“GON”). Inferior RNFL loss corresponding to superiorvisual field loss is a typical pattern found in early GON. Thepredominant inferior visual field loss seen in patients with GON and ADwould correspond structurally to superior RNFL losses. A specificpattern of superior RNFL loss could be detected by using the PS-OCTconfigurations in patients with early AD.

In surgical grafting during reconstructive surgery, the PS-OCTconfigurations may be applied to aid alignment of collagen fiber axes.Coronary artery bypass grafting (“CABG”) is the most commonly performedmajor surgery and a critical determinant of its outcome has beenpostulated to be injury to the conduit vessel incurred during theharvesting procedure or any pathology preexistent in the harvestedvessel. Intravascular PS-OCT imaging from the radial arteries (“RA”)and/or saphenous veins may reliably detect atherosclerotic lesions inthe RAs and discerns plaque morphology as fibrous, fibrocalcific, orfibroatheromatous. The PS-OCT configurations can also be used toidentify patent or healthy regions in longitudinal sections of radialarteries or saphenous veins for grafting

The PS-OCT configurations may be used for margin detection in bronchialtumors. The PS-OCT configurations may also perform early diagnosis oftumors and cancerous tissue. The PS-OCT configuration images mayidentify bronchial tumor presence as destructive growth by ignoring andeffacing normal tissue boundaries. Featureless PS-OCT configurationimages or regions with reduced form-birefringence may lack the orderedmultilayered appearance of the healthy airway wall. The PS-OCTconfigurations may also differentiate between areas of chronicinflammation and invasive malignancy; where the clear demarcations ofepithelium and lamina propria may be observed at inflamed sites and maybe lost in presence of invasive neoplasia. The PS-OCT configurations mayindividually define the epithelium, subepithelial components, andcartilage. The PS-OCT configurations may identify morphologic changesassociated with inflammatory infiltrates, squamous metaplasia, and tumorpresence.

The PS-OCT configurations may assess the coronary plaque collagencontent. Arterial plaques include intimal collagen, which degrades andleads to plaque destabilization. Collagens are major structuralcomponents of the arterial wall extracellular matrix, comprising 20%-50%of the dry weight, with the predominant types being Type I and III,where type IV is in the basement membrane. The tensile strength ofplaque is determined by fibrillar collagen (type I) and extracellularlipid. Inflammation leads to release of collagenases and collagenbreakdown increasing the risk of plaque rupture. Collagen birefringenceis a function of highly organized alignment and also the nature of thechemical groups of the collagen encountered and layer thickness.Form-birefringence is almost exclusively a function of the fibrousnature of the structure and two refractive indices of the fiber andsurrounding material. The intimal region over the necrotic core exhibitshigh polarization sensitivity with organized collagen. The PS-OCTconfigurations may assess plaque collagen content. For example, thefibrous cap is a layer of fibrous connective tissue is thicker and lesscellular than the normal intima. The fibrous cap contains macrophagesand smooth muscle cells. The fibrous cap of an atheroma is composed ofsmooth muscle cells, macrophages, foam cells, lymphocytes, collagen andelastin.). The PS-OCT configurations may assess plaque collagen contentand generate high resolution structural assessments to identify the thincaps associate with high risk plaques.

EXAMPLES

The following examples are put forth so as to provide those of ordinaryskill in the art with a complete disclosure and description of how thearticles, devices, systems, and/or methods claimed herein are made andevaluated, and are intended to be purely exemplary and are not intendedto limit the scope of articles, systems, and/or methods. Efforts havebeen made to ensure accuracy with respect to numbers (e.g., amounts,temperature, etc.), but some errors and deviations should be accountedfor.

Example 1 Phase Retardation and Fast-Axis Angle of a Birefringent Sample

A mica retarder (Meadowlark Optics) is positioned in the common-pathspectral interferometer 10, as shown in FIG. 1, orthogonal to thedirection of incident light propagation and used as a birefringentsample.

FIG. 3A depicts the typical spectral output intensity of a mica retarderpositioned in the common path fiber based single channelpolarization-sensitive spectral interferometer orthogonal to thedirection of incident light propagation and used as a birefringentsample. The output spectral width of the whole spectrum was 12.2 THz, asshown in FIG. 3A. FIG. 3B depicts a small segment of 10 Ghz between190.69 and 190.79 THz of the whole spectrum (12.2 THz) to view fringesin more detail. The output spectrum in FIGS. 3A and 3B is modulated withseveral distinct high frequencies, and a swept source and OSA with highresolution are required to avoid undersampling. A conventional OSA witha spectral resolution of Δλ=0.1 nm provides a scan range of about 12 mmand is unable to sample sufficiently a spectral modulation of such highfrequency.

FIGS. 4A and 4B shows the Fourier transform magnitude of interferencefringes between the front and back surfaces of the glass window, asshown in FIG. 4A, and between the back surface of the glass window andthe birefringent sample, as shown in FIG. 4B. Although the ISA providesthe corresponding optical frequency for each recorded spectral componentof output intensity, successive spectral samples of output intensity arenot equally spaced in optical frequency. In such cases of non-uniformfrequency sampling, a Nonuniform Fourier Transform (“NUFT”) algorithmwas used rather than a simple fast Fourier transform, which assumesuniform sampling. As shown in FIG. 4A, four Stokes spectral componentsof interfering light are separated into seven peaks in the opticalpath-length difference domain. The position of the fourth peak andspacing between peaks are determined by the optical path lengthdifference between interfering beams generated in the common-pathspectral domain interferometer and phase retardations due to the two PMfiber segments in the FOSPI, respectively. In FIG. 4A, the first sevenpeaks are formed from interference between the back surface of the glasswindow and the font surface of the birefringent sample and are similarto those from interference between the front and the back surfaces ofthe glass window in FIG. 4A, indicating the polarization state betweenthe window and the sample is unchanged. Alternatively, the rightmostseven peaks in FIG. 4B resulting from interference between the backsurface of the birefringent sample show the polarization-state change ofdouble-pass light propagation through the birefringent sample.

Phase retardation due to birefringence, as shown in FIG. 5A, andfast-axis angle, as shown in FIG. 5B, of the birefringent sample wereestimated from interference between the back surface of the glass windowand the back surface of the birefringent sample by using equations (13)and (14). For this measurement, the birefringent sample was rotated in 5degrees increments from 0 degrees to 90 degrees. An estimatedsingle-pass phase retardation of δ=34.06 degrees +/−2.68 degrees isconsistent with a valued deduced from the manufacturer's specification(31.4 degrees). The estimated fast-axis angle was offset by 87.5 degreesto the reference with respect to the laboratory coordinate system.

Incorporation of a FOSPI 50 into a common-path spectral interferometer30 with a broadband frequency-swept laser source allows measurement ofthe polarization and depth information with a single optical frequencyscan. Spectral modulations introduced by the common-path spectralinterferometer and by the FOSPI combine sequentially so that thepolarization and depth information are encoded into separate channels inthe time-delay domain. For the single optical frequency scan, multiplescans are required to average out polarimetric speckle noise, asdescribed above. Multiple scans may be implemented to average outpolarimetric speckle noise—as described above. Output from the fiberbased single channel polarization sensitive spectral interferometer is aconvolution of the FOSPI output and that from the common path spectralinterferometer.

The full set of Stokes parameters of interfering light at a specificoptical path-length difference consists of seven channels in thetime-delay domain, and channel separation is dependent on two factors:spectral resolution (Δv) of the instrument and choice of PM fiberlengths in the FOSPI. For one embodiment, a general bulk optical elementdoes not require PM fibers as mentioned above. For another embodiment ofthe fiber-based single-channel polarization-sensitive spectralinterferometer, channel separation is Δτ=3.7 ps and is set by lengths ofthe PM fiber segments. Maximum channel separation in the time delaydomain is inversely related (Δτ max=⅛Δv) to the spectral resolution ofthe instrument, and the broadband frequency-swept laser source (Δv=50MHz) used here allows Δτmax=2.5 ns. Such large channel separations inthe time delay domain require optically stable kilometer-length PM fibersegments in the FOSPI. The sample used here is optically transparent,and its optical thickness is large enough so that the two sets of sevenchannels due to refraction from the front and back surfaces aresufficiently separated. In general, the bandwidth of each peak in thetime delay domain is determined by the optical thickness of the sample,and wide channel separation in the time delay domain is required toisolate each channel.

Prior knowledge of the incident polarization state is not required todetermine phase retardation and fast-axis angle of a birefringent samplein the fiber based single channel polarization sensitive spectralinterferometer. An assumption of no polarization transformation betweenthe reference and sample surfaces is necessary in the analysis, which iseasily achieved in a common path spectral interferometer.

Difference in Stokes parameters determined from the reference andinterference fringe signals are optical path-length difference [Δ(v)]and the phase retardation [δ(v)] of a birefringent sample. If a sampleis non birefringent, Stokes parameters of an interfering fringe signalare S_(i) ^((i))=cos Δ(v)S_(i) ⁽¹⁾(v) with Stokes parameters of lightreflected from the reference surface S_(i) ⁽¹⁾(v) and an opticalpathlength difference Δ(v). Integration of a common-path spectralinterferometer with a FOSPI at the output enables measurement of theStokes parameters of the interference signal with neither a calibrationcorrection factor nor any assumption of polarization state of reflectedlight from the reference surface.

As shown in FIGS. 5A and 5B, phase retardation and fast-axis angle of abirefringent sample are difficult to measure when the direction of anincident light oscillation is primarily parallel to the fast axis of thesample retarder. In this case, the polarization state of light enteringthe interferometer should be modified. Such modification can beimplemented by the input polarization state preparation optics 20inserted between the reference and the sample surfaces, the segment canbe considered a known portion of the birefringent sample with aspecified polarization transformation, and the analysis presented may bemodified to determine the birefringence and fast axis of a sample. Suchan analysis is presented in the paper by Kemp, N.J. et. al. Opt. Express2005: 13:4507, herein incorporated by reference.

Exemplary Conclusion

The FOSPI 50 is a PM fiber based instrument to measure the polarizationstate of collected light and incorporation of the FOSPI 50 into acommon-path spectral interferometer 30 allows measurement of the fullset of Stokes parameters of interfering light with a single opticalfrequency scan where multiple A-scans are required to averagepolarimetric speckle noise unless multiple A-scans are required toaverage polarimetric speckle noise as indicated above. The high spectralresolution of the broadband frequency swept laser source enablesencoding and decoding both the polarization and depth information intoseparate channels in the time delay domain.

Performance of the fiber based single channel polarization sensitivespectral interferometer has been demonstrated by measuring phaseretardation δ and fast axis angle α of a mica retarder while rotated in5° increments from 0° to 90°. A single optical frequency scan issufficient to estimate both phase retardation and fast axis angle of amica plate without knowledge of the polarization state of incidentlight. The fiber based single channel polarization sensitive spectralinterferometer presented allows measurement of both phase retardationand fast axis angle of a birefringent sample. Performance of the fiberbased single channel polarization sensitive spectral interferometer issensitive to phase retardations due to two PM fiber segments in a FOSPI((φ₁(v) and (φ₂(v) in Equation 4). The PS-OCT configurations mayminimize variations in phase retardations induced by environmental,mechanical and thermal fluctuations.

The coupling of a thermally isolated mechanical enclosure to thepolarization sensitive spectral interferometer improves the stability ofPM fiber phase retardations (φ₁(v) and (φ₂(v)). Also, by selectingoptimal optics for the frequency range of the broadband laser source thesignal-to-noise ratio of the system is improved. By using the end facetof the sample path illuminating fiber instead of the glass window,un-wanted and deleterious backscattered signal can be avoided. Slow scanspeed of 1 Hz of the current system can be a limitation in someapplications especially that require time-resolved measurements. Also,the experimental results, i.e., estimated phase retardation and fastaxis angle of a birefringent sample, may be sensitive to post signalprocessing especially when the instrument is not optimized. Fouriertransformation followed by processing in the optical pathlength domainand simple arithmetic are used in the present analysis to determinephase retardation and fast axis angle. Alternatively, a model-basedapproach may provide estimates of position of reflecting surfaces andbirefringence properties. The proposed methodology may be applied tomeasure in real time the depth resolved polarization state ofback-reflected light from a variety of samples.

Example 2 High-Sensitivity Determination of Birefringence in TurbidMedia

Polarimetric Speckle Noise Reduction

Many signal processing applications employ ensemble averaging of Nseparate trials for reducing additive white noise in recorded signals bya factor of N^(1/2). As shown in FIGS. 10A and 10B, averaging N_(A)uncorrelated speckle fields reduces polarimetric speckle noise(σ_(speckle)) and increases PSNR by a factor of N_(A) ^(1/2). Sixfoldincrease in PSNR is demonstrated after averaging Stokes vectors forN_(A)=36 speckle fields in a birefringent film. FIG. 10B is a Poincarésphere before (thin line 320) and after (thick line 322) averagingN_(A)=36 speckle fields for birefringent film S_(m)(z) for m=1 plottedon the Poincaré sphere, where averaged S(z) begins to resemble thenoise-free model polarization arc P(z).

Birefringent Film Measurement

To verify operation of the PS-OCT configuration and the multi-statenonlinear algorithm, horizontal and vertical interference fringeintensities (Γ_(k)(z) and Γ_(v)(z)) were recorded from a turbidbirefringent film (New Focus, #5842) with thickness Δz=80 μm. Atransparent mica waveplate was placed on top of the birefringent film totest the multi-state nonlinear algorithm in the presence of a precedingbirefringent element with unitary transformation. PSNR was increased byaveraging Stokes vectors from Equation (48)

$\begin{matrix}{{\overset{->}{S}\left( z_{j\;} \right)} = {\begin{pmatrix}{I\left( z_{j} \right)} \\{Q\left( z_{j} \right)} \\{U\left( z_{j} \right)} \\{V\left( z_{j} \right)}\end{pmatrix} = {\begin{pmatrix}{{E_{h}\left( z_{j} \right)}^{2} + {E_{v}\left( z_{j} \right)}^{2}} \\{{E_{h}\left( z_{j} \right)}^{2} - {E_{v}\left( z_{j} \right)}^{2}} \\{2\; {E_{h}\left( z_{j} \right)}{E_{v}\left( z_{j} \right)}{\cos \left\lbrack {\varphi_{diff}\left( z_{j} \right)} \right\rbrack}} \\{2\; {E_{h}\left( z_{j} \right)}{E_{v}\left( z_{j} \right)}{\sin \left\lbrack {\varphi_{diff}\left( z_{j} \right)} \right\rbrack}}\end{pmatrix}.}}} & (48)\end{matrix}$

from N_(A)=36 uncorrelated speckle fields within a small two-dimensionalsquare grid region (50×50 μm). Depth-resolved polarization data[S_(m)(z)] was plotted on the Poincaré sphere for M=6 incidentpolarization states. To demonstrate invariance of the multi-statenonlinear algorithm to a preceding birefringent element, δ of thebirefringent film is determined for a range of mica waveplate slow-axisorientations ranging from 0° to 180° in increments of 10°.

Retardation (δ) of the birefringent film was determined for a range ofmica waveplate slow-axis orientations ranging from 0° to 180° inincrements of 10°. Mean and standard deviation of δ over the range ofmica waveplate orientations was δ=24.50°±0.47°, while maximum deviationfrom the mean was 0.91°. Mean birefringence was Δn=7.0·10⁻⁴ or 30.6°/100μm.

In Vivo Primate Retinal Nerve Fiber Layer Measurement

The PS-OCT configuration is described in previously and the multi-statenonlinear algorithm to detect RNFL birefringence and biattenuance,respectively. Γ_(h)(z_(j)) and Γ_(v)(z_(j)) were recorded from the RNFL.All experimental primate procedures were approved by the University ofTexas at Austin Institutional Animal Care and Use Committee (protocol#02032203) and conform to all USDA, NIH, and ARVO guidelines for animalwelfare.₁₅₁ Both eyes of two healthy 6 kg, 4 year old, female rhesusmonkeys were imaged. Monkeys were anesthetized with a combination ofketamine (10 mg/Kg) and xylazine (0.25 mg/Kg) given intramuscularly.Anesthesia depth was monitored and maintained by a certified veterinarytechnologist. Pupils were dilated using one drop of 1% cyclopentolateand one drop of 1% tropicamide. The head was gently secured to agoniometer in the prone position using a custom mask. One drop of 10%methylcellulose was placed in the eye to be imaged and a contact lenswas placed on the eye. The contact lenses were chosen to render themonkeys slightly myopic so incoming light was focused at the innerlimiting membrane. Specifications of the contact lens were: basecurve=6.9 mm, diameter=8.6 mm, power=+2 diopter. The retina was viewedusing a surgical microscope and the eye was rotated and held in positionby a Thornton fixation ring. A coaxial visible aiming beam was placeddirectly onto the optic nervehead for registration at the start of eachscan. Sample arm optics were configured for pupil-centric scanning Priorto recording high resolution maps, a low-resolution fast scan wasperformed to insure the selected lateral area included all desiredperipapillary features.

The data acquisition time to record a single peripapillary map may varyaccording to the optical configuration; however, the time to record thedata may not be that important inasmuch as longer acquisition times aredesired. Laser power incident on the cornea was 2.8 mW during lateralscanning and 1.7 mW while stationary. Approximate laser spot size at theretinal surface was 30 μm. Axial resolution was determined by the 5 μmcoherence length of the laser source in air. Lateral scanning in the xand y dimensions allowed acquisition of Γ_(h)(z_(j)) and Γ_(v)(z_(j)) attwo user-specified locations: 1 mm inferior to the center of the ONH and1 mm nasal to the center of the ONH. At each location, Γ_(h)(z_(j)) andΓ_(v)(z_(j)) were recorded for an ensemble of N_(A)=36 uncorrelatedspeckle fields in a small two-dimensional square grid region (50 μm×50μm). Registration of the imaging location between sessions wasaccomplished by positioning the eye with the center of the ONH at thezeroed position of the visible aiming beam.

The anterior surface of the RNFL (z_(j)=0) was determined automaticallyby thresholding, and the posterior RNFL surface was identified manuallyfrom the depth-resolved interference fringe intensity [I(z_(j))]. Thedifference between posterior and anterior surfaces (optical RNFLthickness) was divided by the mean group tissue refractive index(n=1.38) to determine RNFL thickness (Δz_(RNFL)). Stokes vectors withinthe ensemble were digitally averaged, normalized, and plotted on thePoincaré sphere for M=6 incident polarization states. The multistatenonlinear algorithm was applied to extract P(z_(j)) from S(z_(j)) anddetermine in vivo primate RNFL retardation (δ_(RNFL)) and birefringence(Δn_(RNFL)).

The primate RNFL was imaged in a thick region (1 mm inferior to thecenter of the ONH) and a thin region (1 mm nasal to the center of theONH) during two sessions two weeks apart. Table 1 summarizes thedetected RNFL ΔZ_(RNFL), δ_(RNFL) and Δn_(RNFL) given in units ofdegrees per 100 micrometers. FIGS. 11A and 11B shows PS-OCT-recordedS_(m)(z) for M=6 incident polarization states and correspondingP_(m)(z_(j)) extracted by the multistate nonlinear algorithm. Noise-freemodel polarization arcs [P_(m)(z), black] and rotation axis (A) wereextracted by the multi-state nonlinear algorithm. Arcs corresponding toM=3, 4, and 5 are on the far side of the Poincaré sphere in FIGS. 11Aand 11B.

TABLE 1 Thickness and Birefringence of in Vivo Primate RNFL Location(session) Δz_(RNFL) (mm) δ_(RNFL) (°) Δn_(RNFL) (°/100 μm) Inferior(day 1) 170 29.5 17.3 Inferior (day 2) 167 27.8 16.6 Nasal (day 1) 503.4 6.8 Nasal (day 2) 51 3.9 7.6

Ensemble averaging to increase PSNR comes with a loss in lateralresolution, increase in acquisition time by a factor of N_(A), anddiminishing returns associated with the N_(A) ^(1/2) relationship. Lossin lateral resolution is from the increase in the field sizecorresponding to lateral extent of uncorrelated speckle fields includedin the averaged ensemble. Because speckle noise statistics are closelyrelated to the beam diameter, detection optics, and microstructure ofscatterings in the specimen, each instrument-specimen combination has anoptimum spacing between speckle fields which minimizes loss in lateralresolution but insures speckle fields are uncorrelated.

The N_(A) ^(1/2) behavior of averaged polarimetric speckle noise allowstrial-and-error discovery of the optimum spacing between speckle fieldswithout a priori knowledge of the scatterer microstructure. The optimumspacing between speckle fields for imaging the birefringent film withour system was determined empirically (8 μm). Larger spacing results inreduced lateral resolution and smaller spacing leaves speckle fieldspartially correlated thereby diminishing the N_(A 1/2) noise reductionachieved through ensemble averaging. The likelihood of combiningpolarization data from adjacent anatomical features is decreased withmarginal additional instrumentation complexity by averaging over a smalltwo-dimensional square grid region rather than a pattern of traditionalrastered B-scan.

The choice of M=6 incident polarization states in these results wasselected empirically. Because switching time of the LCVR is negligiblecompared to total acquisition time, acquiring M incident polarizationstates increases imaging time by a factor of M. Although selection of anincident polarization state with γ=90° may be achieved using analysis ofprior polarization arcs, this would require additional computingresources (e.g. automatic segmentation, real-time nonlinear fitting) andimprovements in speed and accuracy may be marginal. Increasedacquisition time by a factor of N_(A)×M, although problematic during invivo imaging with slow time-domain systems is not a limiting factor forinstruments incorporating spectral-domain approaches.

Results of the birefringent film experiments indicate the multi-statenonlinear algorithm may be applied to determine retardation in turbidbirefringent media. Moreover, determination of δ by the multi-statenonlinear algorithm is invariant to unknown unitary polarizationtransformations from preceding birefringent layers as demonstrated bythe mica waveplate rotation.

Sources of error in birefringence calculation include (1) uncertainty inthe bulk refractive index (±2.5%); and (2) uncertainty in δ due topolarimetric speckle noise which lingers after ensemble averaging. Afteraveraging N_(A)=36 speckle fields, polarimetric speckle noise wascalculated [Eq. (16)] to be σ_(speckle)=4°, resulting in an approximatedouble-pass retardation uncertainty of ±2° or a single-pass retardationuncertainty of ±1°. Uncertainty estimated using the mean error betweenvariable birefringent phantom measurements and linear fit was ±1°. Theseuncertainties give error bars on the RNFL birefringence measurements andalso a quantitative value for the birefringence sensitivity of thePS-OCT configuration, as shown in FIG. 12. Additional averaging(N_(A)>36) would decrease uncertainty in δ and further increase thesensitivity of PS-OCT configuration, but with a cost of decreasedlateral resolution and increased acquisition time.

Example 3 Form-Biattenuance in Fibrous Tissues

Ex Vivo Rat Tendon Measurements

Four mature, freshly-euthanized Sprague-Dawley rats were obtained. Tocollect tail tendon specimens, each tail was cut from the body and alongitudinal incision the length of the tail was made in the skin on thedorsal side Skin was peeled back and tertiary fascicle groups wereextracted with tweezers and placed in phosphate buffered saline solutionto prevent dehydration before imaging. Anatomical terminology used isconsistent with the structure of the rat tail tendon. Tertiary fasciclegroups were teased apart into individual fascicles with tweezers andplaced in a modified cuvette in the sample path of the PS-OCTconfiguration. The cuvette maintained saline solution around thefascicle, prevented mechanical deformation in the radial direction, andallowed 20 g weights to be attached at each end of the fascicle. Weightsprovided minimal longitudinal loading in order to flatten the collagenfibril crimp structure present in rat tail tendon. A total of 111different fascicle locations were imaged from the four rats, each at thelocation of maximum diameter across its transverse cross-section (asdetermined by an OCT B-scan image). Achilles tendon specimens from thesame rats were harvested in a straightforward manner and imaged whilepositioned in the modified cuvette with the same loading conditions.Four different Achilles tendons were imaged in 45 different randomlychosen locations. S_(m)(z) was recorded (N_(A)=64, M=3) at all locationsand the multistate nonlinear algorithm estimated ∈ and δ for eachlocation.

To investigate effect of relative depth of light focus within the tissueon the estimated values for δ and ∈, the same location on a single rattail tendon fascicle was imaged for a range of axial displacementsbetween the rear principal plane of the f=25 mm focusing lens and thefascicle surface. S_(m)(z) (N_(A)=64, M=3) for ten 50-μm-steps from 0(focused at surface) to 450 μm (focused deep within fascicle) wasrecorded.

To investigate effect of different initial separation-angles [γ_(m)(0)]on the PS-OCT-estimated values for δ and ∈, a ⅙-wave retarder was placedin the sample path between the LCVR and scanning optics and S_(m)(z)(N_(A)=64, M=5) recorded from the same location on a single rat tailtendon fascicle for 12 uniformly spaced orientations (between 0° and165°) of the ⅙-wave retarder fast-axis.

For 111 locations in rat tail tendon, mean±standard deviation and[range] in rat tail tendon form-biattenuance wereΔ_(χ=)5.3·10⁻⁴±1.3·10⁻⁴[3.0·10⁻⁴, 8.0·10⁻⁴] and in form-birefringencewere Δn=51.7·10⁻⁴±2.6·10⁻⁴[46.8·10⁻⁴, 56.3·10⁻⁴]. FIGS. 13A-B and 14A-Bshow S_(m)(z) and P_(m)(z) plotted on the Poincaré sphere for twodifferent rat tail tendon fascicles with the largest (Δχ=8.0·10⁻⁴), asshown in FIGS. 13A-B, and smallest (Δ_(χ)=3.0·10⁻⁴), as shown in FIGS.14A-B form-biattenuances detected. Form birefringence for the twofascicles shown in FIGS. 13A-B and 14A-B were Δn=47.4·10⁻⁴ andΔn=55.2·10⁻⁴ respectively. Polarimetric signal-to-noise ratio (PSNR)ranged from 51 to 155 and standard deviation of polarimetric specklenoise (σ_(speckle)) was approximately 0.22 rad for the 111 rat tailtendon locations measured. A single incident polarization state (m=1) isshown for simplicity. (a) S_(m)(z) for tendon with relatively highform-biattenuance (Δ_(χ)=8.0·10⁻⁴) collapses toward {circumflex over(β)} faster than that for (b) tendon with relatively lowform-biattenuance (Δ_(χ)=3.0·10⁻⁴).

Variation in Form-Biattenuance Versus Relative Focal Depth

For 10 different displacements between the rear principal plane of thef=25 mm focusing lens and the fascicle surface, σ_(speckle)≈0.22 rad andmean±standard deviation in relative-attenuation were ∈=1.42±0.022 radand in phase retardation were δ=11.5±0.034 rad. Thickness of the tendonspecimen was Δz=360 μm.

Variation in Form-Biattenuance Versus ⅙-Wave Retarder Axis Orientation

For 12 orientations of the ⅙-wave retarder axis, mean±standard deviationin relative-attenuation were ∈=1.54±0.096 rad and in phase retardationwere δ=13.1±0.046 rad. σ_(speckle) increased exponentially from 0.066rad for a small initial separation-angle of γ_(m)(0)=0.81 rad up toσ_(speckle)=0.69 rad for a large γ_(m)(0)=3.0 rad. Thickness of thetendon specimen was Δz=383 μm.

Rat Achilles Tendon

For 45 locations in rat Achilles tendon, mean±standard deviation and[range] in rat Achilles tendon form-biattenuance wereΔ_(χ)=1.3·10⁻⁴±0.53·10⁻⁴ [0.74·10⁻⁴, 3.2·10⁻⁴] and in form-birefringencewere Δn=46.9·10⁻⁴±5.9·10⁻⁴ [32.9·10⁻⁴, 56.3·10⁻⁴]. FIGS. 15A-B showsS_(m)(z) and P_(m)(z) plotted on the Poincaré sphere for the location inwhich the form-biattenuance was the lowest of all tendon specimensstudied (Δ_(χ)=0.74·10⁻⁴). PSNR ranged from 76 to 175 andσ_(speckle)≈0.20 rad for the 45 rat Achilles tendon locations measured.

A single incident polarization state (m=1) is shown for simplicity.Form-biattenuance in this specimen (Δ_(χ)=3.2°/100 μm) is lower than forspecimens shown in FIGS. 13A-B and 14A-B and spiral collapse toward{circumflex over (β)} is correspondingly slower.

Ex Vivo Chicken Tendon Measurements

57 randomly chosen locations were imaged from tendons extracted from theproximal end of chicken thighs obtained at a local grocery store.Temperature variations (freezing/thawing or refrigeration) andpostmortem time prior to characterization by PS-OCT were unknown.Extracted tendon specimens were kept hydrated in the modified cuvetteand imaged without mechanical loading. S_(m)(z) was recorded (N_(A)=64,M=3) at all locations and the multistate nonlinear algorithm was used toestimates ∈ and δ for each location.

For 57 locations in chicken drumstick tendon, mean±standard deviationand [range] in chicken drumstick tendon form-biattenuance wereΔ_(χ)=2.1·10⁻⁴±0.3·10⁻⁴[1.4·10⁻⁴, 3.1·10⁻⁴] and in form-birefringencewere Δn=44.4·10⁻⁴±1.9·10⁻⁴ [38.4·10⁻⁴, 48.4·10⁻⁴]. PSNR ranged from 42to 96 and σ_(speckle)≈0.28 rad for the 57 chicken drumstick tendonlocations measured.

In Vivo Primate Retinal Nerve Fiber Layer Measurements

Details of the animal protocol for PS-OCT characterization of the invivo primate retinal nerve fiber layer (RNFL) were given in EXAMPLE 2.S_(m)(z) was recorded (N_(A)=36, M=6) on two different days for sixlocations distributed in a 100 μm region around a point 1 mm inferior tothe optic nerve head (“ONH”) center and six locations distributed in a100 μm region around a point 1 mm nasal to the ONH center.

The mean±standard deviation and [range] in form-biattenuance for the sixlocations within a 100 m region around a point 1 mm inferior to the ONHcenter: φ_(χ)=0.18·10⁻⁴±0.09·10⁻⁴ [0.07·10⁻⁴, 0.33·10⁻⁴] on day 1 andΔ_(χ)=0.18·10⁻⁴±0.13·10⁻⁴ [0.06·10⁻⁴, 0.42·10⁻⁴] on day 2. Average RNFLthickness in this region was 166 μm and average relative-attenuation (∈)was 0.023 radians. FIG. 16A shows typical S_(m)(z) and P_(m)(z) plottedon the Poincaré sphere for the region 1 mm inferior to the ONH center inthe primate RNFL. PSNR ranged from 3 to 16 and σ_(speckle)≈0.06 rad forthe six inferior locations measured. In the region 1 mm nasal to the ONHcenter, RNFL thickness averaged 50 μm and PSNR was too low for reliableestimates of Δ_(χ) in the nasal region of the primate RNFL. The RNFLexhibits only a fraction of a wave of phase retardation compared tomultiple waves exhibited by tendon specimens in FIGS. 13A and 14A.

Variation in Measurements of Form-Biattenuance

Uncertainty in phase retardation (u_(δ)) is predominantly due topolarimetric speckle noise (σ_(speckle)) which lingers afterensemble-averaging. Arc length (l_(arc)) has approximately the samefunctional dependence on δ and ∈, therefore uncertainty inrelative-attenuation (u_(∈)) is expected to be similar to u_(δ) for agiven σ_(speckle), though additional experiments in a controlled modelare necessary to verify the relationship between u_(∈), u_(δ), andσ_(speckle). Uncertainties in form-birefringence (u_(Δn)) orform-biattenuance (u_(Δ) _(χ) ) are dependent on u_(δ) or u_(∈) as wellas the specimen thickness (Δz), which complicates comparison of u_(Δn)or u_(Δ) _(χ) between specimens or between other variations of PS-OCTconfiguration. For the rat and chicken tendon specimens studied(N_(A)=64), σ_(speckle) ranged from 0.20 to 0.28 rad, givinguncertainties (u_(δ) and u_(∈)) due to polarimetric speckle noise nohigher than ±0.07 rad. Corresponding uncertainty in form-biattenuancefor a Δz=160-μm-thick specimen is u_(Δ) _(χ) ±0.57.1e. In primate RNFL(N_(A)=36), σ_(speckle)≈0.06 rad corresponds to u_(∈)≈±0.015 rad oru_(Δ) _(χ) ≈±0.12·10⁻⁴ for an RNFL thickness of Δz=166 μm.

The range of systematic variation in measurements of δ and ∈ due toplacement of the beam focus was negligible. Variation in measured ∈(6.2%) due to different initial separation-angles [γ_(m)(0)] was higherthan variation in δ (0.35%). Interestingly, σ_(speckle) has a roughlyexponential dependence on γ_(m)(0). Large initial separation angles[γ_(m)(0)≈π] correspond to incident polarization states [S_(m)(0)] nearthe preferentially attenuated eigenpolarization; therefore, it isexpected that these S_(m)(0) will have lower detected intensity andrelatively higher noise variation on the Poincaré sphere than S_(m)(0)with lower γ_(m)(0). Additional experiments may characterize completelythe dependence of σ_(speckle) on γ_(m)(0). Because W_(m)(z) [Eq. (33)]decreases with increasing σ_(speckle), states with large γ_(m)(0) areweighted less by the multistate nonlinear algorithm when estimating δand ∈. Inspection of the FIGS. 13B, 14B, 15B, and 16B reveals thatσ_(speckle) does not increase significantly versus depth (z) for thelimited tissue thicknesses studied. Therefore, it is not expected thatreduced collection of light backscattered from deeper in the tissuesignificantly affects the estimates of ∈ for the range of depths probed.

Form-Biattenuance Comparison with Other Values

The form-biattenuance values measured in tendon are significantly higherthan those approximated from D/Δz values reported in chicken tendon(Δ_(χ)=0.8·10⁻⁴) or in porcine tendon (Δ_(χ)=0.17·10⁻⁴). The range ofΔ_(χ) values measured in a substantial number of specimens of rat tailtendon (3.0·10⁻⁴ to 8.0.104 for N=111), rat Achilles tendon (0.74·10⁻⁴to 3.2·10⁻⁴ for N=45), and chicken drumstick tendon (1.4.104 to 3.1·10⁻⁴for N=57) demonstrate that a sizable inter-species and intra-speciesvariation is present in tendon form-biattenuance.

Loading the tendon specimens with 20 g weights was to extract tendonexhibits with a well-known crimp structure in which the constituentcollagen fibers are not regularly aligned. Applying a small load to thetendon effectively flattens the crimp, providing a reproducible specimenwhich can be modeled using the Jones matrix in Eq. (30) for ahomogeneous linear retarder/diattenuator and giving results that can beobjectively compared. And the in vivo state of tendon is more similar tothe slightly loaded state than to a completely relaxed or non-loadedstate, especially considering that even minimal muscle tone would causeslight tension in connected tendons. Variance in the measurements of rattail tendon biattenuance and birefringence was substantially reduced byloading, but mean Δ_(χ) and Δn was not noticeably affected. For thepurpose of comparison with previous results on chicken tendon, chickentendon specimens were not mechanically loaded. Measured values ofform-biattenuance of chicken tendon (Δ_(χ)≧1.4·10⁻⁴) are nearly a factorof two higher than previously reported (Δ_(χ)=0.8·10⁻⁴).

Because the small-angle approximation introduces only minimal error inpreviously reported values of D/Δz, discrepancy with Δ_(χ) values is notdue to conversion from diattenuation (D) to relative-attenuation (∈).Difference in values may be due to wide inherent anatomical variation inform-biattenuance, nonstandard tissue extraction and preparation, orlarge uncertainty in the methodologies. Details such as tissuefreshness, anatomical origin of the harvested specimens, and detaileddescription of the expected uncertainty are not available. Additionally,crimp structure present in non-loaded tendon specimens could causespatial variations in collagen fiber orientation over the sample beamdiameter, resulting in poor agreement with a homogeneous linearretarder/diattenuator model [Eq. (30)] and artifacts in measurements ofΔ_(χ).

The validity of using diattenuation-per-unit-depth (D/Δz) as anapproximation for ∈/Δz (or Δ_(χ)) is dependent on the acceptableuncertainty for a particular application. For example, using the rattail tendon results presented (∈=1.54±0.096 rad), the percentage erroris 6.2% due to ⅙-wave retarder orientation. Using Eq. (31), thecorresponding diattenuation is D=tanh(1.54)=0.91. Because c increaseslinearly with depth, this tendon (Δz=383 μm) hasrelative-attenuation-per-unit-depth of ∈/Δz=1.54 rad/383 μm=0.004 rad/μmor form-biattenuance Δ_(χ)=5.3·10⁻⁴. Expressing this asdiattenuation-per-unit-depth D/Δz=0.91/383 μm=0.0024/μm results in anerror of 40%, which is much higher than the next largest error source(6.2%) and may be unacceptable for many applications. Additionalreduction in σ_(speckle) will allow more sensitive determination of ∈.For arbitrarily large PSNR, the small-angle approximation is invalid forany specimen.

Diattenuation by PS-OCT has been primarily concerned with its effect onestimates of phase retardation or form birefringence. The reasonableestimates of phase retardation can be made in tendon and muscle even ifdiattenuation is physically present but is ignored in the model. Indeed,one can discern from the “damped” sinusoidal nature of the normalizedStokes parameters vs. depth (FIGS. 13A-B and 14A-B) that the frequencyof sinusoidal oscillation (proportional to form-birefringence) can beestimated without considering the “damped” amplitude variation (due toform-biattenuance) when multiple periods of oscillation (multiple wavesof phase retardation) are present. Results show that relativecontribution to polarimetric transformations from Δn and Δ_(χ) varieslargely. In rat tail tendon, Δ_(χ)/Δn was measured as high as 0.17 andin Achilles tendon as low as 0.017. In instances where either 1)Δ_(χ)/Δn is high, 2) multiple periods of oscillation are not present, or3) PSNR is low, accuracy in estimates of Δn (Δ_(χ)) will be reduced ifform-biattenuance (form-birefringence) is ignored.

Polarimetric speckle noise (σ_(speckle)) depends on the initialseparation-angle [γ_(m)(0)]. Based on this observation, the number ofincident polarization states (M) and the selection of those states[S_(m)(0)] relative to {circumflex over (β)} employed by a particularPS-OCT approach will affect the ability to accurately distinguishbetween Δn and Δ_(χ). Approaches using M=2 incident polarization stateswhich are positioned orthogonally to each other in their representationon the Poincaré sphere and are suited for detecting δ and Δn.Alternatively, M=2 polarization states which are oriented parallel andperpendicular to the optic axis in physical space (and opposite to eachother in their representation on the Poincaré sphere) may provide thebest estimates of ∈ and Δ_(χ). These considerations suggest thatselecting at least M=3 incident polarization states for optimaldetermination of both form-birefringence and form-biattenuance,regardless of the particular PS-OCT approach used. The multistatenonlinear algorithm discriminates between Δn and Δ_(χ) by restrictingcontributions to movement of S_(m)(z) on the Poincaré sphere from eachphenomenon into two orthogonal planes and seamlessly incorporates M=3incident polarization states while avoiding issues related tooverdetermined Jones matrices.

Because form-birefringence and form-biattenuance arise from lightscattering by nanometer-sized anisotropic structures, development ofsophisticated models relating Δn and Δ_(χ) to underlying microstructurewill allow use of the PS-OCT configurations for noninvasively andinvasively quantifying fibrous constituents (e.g., neurotubules in theRNFL or collagen fibers in tendon) which are smaller than the resolutionlimit of light microscopy. A portion of the tendon birefringence may bedue to intrinsic birefringence on the molecular scale. Becausebiattenuance in tendon or RNFL may arise from interactions on thenanometer scale, form-biattenuance and biattenuance may be usedinterchangeably.

The small-angle approximation introduces minimal error fordiattenuation-per-unit-depth (D/Δz≈∈/Δz) observed in thin tissuespecimens (Δz<1 mm). Substantial measurements on tissues have adiattenuation (D) that is outside the range of the small-angleapproximation and cannot be meaningfully reported on adiattenuation-per-unit-depth (D/Δz) basis. Biattenuance (Δ_(χ)) requiresno approximation and is analogous and complementary to a well-understoodterm, birefringence (Δn). Use of the term biattenuance overcomes theneed to specify when a diattenuation-per-unit-depth approximation isvalid. Consistency in definitions between birefringence (Δn) andbiattenuance (Δ_(χ)) or between phase retardation (δ) andrelative-attenuation (∈) allow a meaningful and intuitive comparison ofthe relative values (i.e. Δ_(χ)/Δn, ∈/δ) of amplitude and phaseanisotropy in any optical medium or specimen. The availability of narrowline-width swept-source lasers allows construction of Fourier-domainPS-OCT instruments having scan depths far longer than current PS-OCTinstruments. By using swept laser sources and hyperosmotic agents toreduce scattering in tissue, the PS-OCT configuration probessignificantly deeper into tissue specimens than 1-2 mm, likely makingthe small-angle approximation invalid even in tissues with lowbiattenuance. A narrow line width laser source will allow longer scandistances as described in the common path spectral domain PS-OCTconfiguration. The ability to determine the biattenuance with a spectraldomain approach is dependent on the multi-state fitting algorithm orsimilar approach as described above. The spectral domain approach, asdescribed in the PS-OCT configuration 10 and 200, allows fasteracquisition of the data and provide improved estimates (relative to timedomain systems) of birefringence and biattenuance. PS-OCT characterizesnon-biological samples which may have higher D and not satisfy thesmall-angle approximation. Biattenuance is useful in employing otherpolarimetric optical characterization techniques, which can detectanisotropically scattered light and for which dichroism is thereforeinappropriate. Finally, although the term “depth-resolved” is frequentlyused in the context of either “measured in the depth dimension” or“local variation in a parameter versus depth [e.g., Δ_(χ)(z)]”,biattenuance is independent of the particular interpretation. The firstinterpretation may be applied to biattenuance, but the multistatenonlinear algorithm can be extended in a straightforward manner toprovide local variation in biattenuance versus depth [Δ_(χ)(z)].

Exemplary Conclusion

Biattenuance (Δ_(χ)) is an intrinsic physical property responsible forpolarization-dependent amplitude attenuation, just as birefringence (Δn)is the physical property responsible for polarization-dependent phasedelay. Diattenuation (D) gives the quantity of accumulated anisotropicattenuation over a given depth (Δz) by a given optical element. Thenonlinear dependence of diattenuation on depth motivated introduction ofrelative-attenuation (∈), which depends linearly on depth, maintainsparallelism and consistency with phase retardation (δ) in Eq. (30), andis a natural parameter in depth-resolved polarimetry such as PS-OCT. Themathematical relationships between these parameters were given in Eqs.(27), (29), and (31).

The PS-OCT configurations includes: (1) theoretical and experimentalvalidation for a new term in optical polarimetry, biattenuance (Δ_(χ)),which describes the phenomenon of anisotropic or polarization-dependentattenuation of light amplitudes due to absorption (dichroism) orscattering; (2) detailed mathematical formulation of Δ_(χ) andrelative-attenuation (∈) in a manner consistent with establishedpolarimetry (i.e., birefringence and phase retardation), andmathematical relationships to related polarimetric terms diattenuationand dual attenuation coefficients; (3) analytic expression fortrajectory of normalized Stokes vectors on the Poincaré sphere in thepresence of both birefringence and biattenuance; (4) expression for arclength (l_(arc)) and PSNR of normalized Stokes vector arcs on thePoincaré sphere in the presence of both birefringence and biattenuance;(5) modification of a multistate nonlinear algorithm to providesensitive and accurate estimates of ∈ and Δ_(χ) in addition to δ and Δn;(6) incorporation of a scalar weighting factor [W_(m)(z)] into themultistate nonlinear algorithm; (7) substantial ex vivo and in vivoexperimental data in several species and two tissue types to demonstratelarge variation in Δ_(χ), as well as interpretation of this data in thecontext of previously reported values; (8) description of the expecteduncertainty in our measurements of ∈ and Δ_(χ); and (9) introduction ofa physical model for birefringent and biattenuating optical media.

Form-biattenuance and form-birefringence are closely related butphysically distinct phenomena which may convey different informationabout tissue microstructure. The form-biattenuance diagnosticcapabilities remain with how accurate the determination ofform-biattenuance and form-birefringence are concurrently used inbiomedical research or clinical diagnostics. Form-biattenuance mayquantify the effect of tendon crimp on Δn and Δ_(χ) and to establish theacceptable uncertainty in biattenuance for diagnosis of variouspathological tissue states. Other fibrous tissues at multiple imagingwavelengths may refine the physical model and establish a comprehensiveanatomical range for biattenuance.

Example 4 Fiber Orientation Contrast for Depth-Resolved Identificationof Structural Interfaces in Birefringent Tissue

Procedures for calibrating the constant retardation offset in theinstrument and for preparing the intervertebral disc specimen for PS-OCTimaging were given above. The lateral (x-y dimension) scan pattern usedconsisted of 20 uniformly spaced clusters of N_(A)=36 A-scans (720A-scans total). The N_(A)=36 A-scans in each cluster were acquired inslightly displaced spatial locations on a 6×6 square grid (25 μm×25 μm)to uncorrelate speckle noise. A-scans acquired in this x-y scan patternwere flattened into an intensity B-scan image (I(x, z), FIG. 17),resulting in the slight sawtooth artifact apparent on the specimensurface. No averaging was performed in the intensity B-scan imagedisplayed in FIG. 17. Depth-resolved polarization data (Sm(z)) wasacquired for M=6 different incident polarization states and thenensemble averaging of N_(A)=36 A-scans was performed to reducepolarimetric speckle noise (σ_(speckle)) in each cluster.

For each of the 20 clusters in the x-dimension, the following procedurewas carried out using only the averaged depth-resolved polarization data(S_(m)(z)) for that cluster. First, the top surface of the specimen wasidentified as the depth (z_(top)) at which S_(m)(z) ceased to exhibitrandom noise fluctuations and began tracing regular arcs on the Poincarésphere. Second, depths below Z_(top) at which the trajectories ofS_(m)(z) showed a spike in curvature (κ(z), FIG. 18A-B) were identifiedas discrete changes in fiber orientation and were attributed tointerfaces between lamellae. Only k=3 lamellae for a single incidentpolarization state (m=1) are shown for simplicity in FIGS. 18A-B.Lamellar thickness (Δz_(k)) was recorded as the distance betweeninterfaces for each lamella k and was compensated by the tissuerefractive index (n=1.40). Normalization of Stokes vectors ensures thatintensity contrast information (I(z)) does not contribute toidentification of lamellar interfaces. Data from adjacent clusters werenot used in this procedure.

The high sensitivity nonlinear fitting algorithm in Example 3 was thenapplied to estimate phase retardation (δ₁), relative attenuation (∈₁)and eigenaxis ({circumflex over (β)}₁) for the top lamella (k=1) andthen successive δ_(k), ∈_(k), and {circumflex over (β)}_(k) for k=2 wereestimated after iterative compensation of δ_(k-1) and ∈_(k-1).

Exemplary Results

Fiber orientation (θ_(k)) and birefringence (Δn_(k)) for each lamella kand for all 20 lateral clusters were calculated from Δz_(k), δ_(k) and{circumflex over (β)}_(k) as discussed above and assembled into B-scanimages of depth-resolved fiber orientation (θ(x, z), FIG. 19) andbirefringence (Δn(x, z), FIG. 20). FIG. 19 shows the lamellar structureis clearly visible due to high contrast between fiber orientations insuccessive layers. Relative attenuation (∈_(k)) was at or below thesensitivity limit for the deeper lamellae in this cartilage specimen andtherefore a B-scan image of biattenuance is not shown. The mean andstandard deviation in biattenuance in the thick upper layer where ∈ wasabove the sensitivity limit are Δ_(χ)=1.02×10⁻⁴±0.31×10⁻⁴.

In FIG. 20, black lines indicate lamellar interfaces determined byidentifying segments in trajectories of S_(m)(z) with high curvature(κ(z)). FIG. 21 shows these interfaces superimposed on the originalbackscattered intensity OCT B-scan image (I(x, z)). A sliding averagingwindow (15% of image width) was applied across each interface to smoothblack lines in FIG. 21. Quantitative estimates for mean lamellaethickness (Δ z _(k)) are also indicated in FIG. 21.

The determination of boundaries and lamellar thickness (Δ z _(k)) usingthe trajectory of S_(m)(z) provides vastly improved contrast over I(x,z) in the annulus fibrous specimen, as shown in FIG. 21. Sincebackscattered intensity images do not exhibit adequate contrast fordetecting these structural details, the technique based only on thedepth-resolved polarization state resolves the contrast. This isespecially true in cartilage, a tissue in which these structuresdirectly contribute to mechanical and physiological properties.

Improving contrast and identifying lamellar interfaces by detectingchanges in relative fiber orientation does not require computationallyintensive processing algorithms which are necessary to effectivelyquantify tissue retardation, diattenuation and fiber orientation (suchas fitting of Stokes vector trajectories or Jones matrices). Therefore,the technique is more amenable to real-time image processing necessaryin clinical situations. The B-scan image of fiber axis orientation (θ(x,z), FIG. 19) was constructed using a calibrated PS-OCT configuration andtherefore represents the collagen fiber orientation referencedabsolutely to the horizontal laboratory frame. For identifyinginterfaces using the depth-resolved polarization state method, onlyrelative fiber orientation changes must be detected; thus, a fiber-opticrather than bulk-optic PS-OCT configuration has stability andportability advantages in a clinical environment. The method usingdepth-resolved curvature (κ(z)) of normalized Stokes vectors (S(z)) toidentify boundaries in multiple-layered fibrous tissue can be applied toall phase-sensitive PS-OCT configurations that detect depth-resolvedStokes vectors, whether fiber-based or bulk-optic, single-incident-stateor multi-incident-state, time-domain or frequency-domain. Followingboundary identification, subsequent quantification of fiber orientation(relative or absolute), retardation or diattenuation can be accomplishedusing the method described in EXAMPLES 2 and 3.

Several additional features are apparent in the θ(x, z) and Δn(x, z)B-scan images. First, a small region of reduced birefringence appears inthe middle of the Δn(x, z) image, corresponding to a region withslightly lower backscattering intensity in I(x, z). This may be a regioncontaining lower collagen fiber density. Second, an incomplete lamellawith reduced birefringence is evident in the top right half of thespecimen. Incomplete lamellae are commonly observed in annulus fibrouscartilage. Third, fiber orientation is twisted approximately 15-20°counterclockwise in the right half of the θ(x, z) image relative to theleft half. Finally, increased Δn in the lower left region reveals adifferent collagen fiber structure here.

Optical or electron microscopy histology is well known to not preservein situ dimensions due to the dehydration process integral inhistological preparation and therefore is valuable only forcorroboration of general tissue morphology in OCT images. Althoughhistology is the gold standard for pathological diagnoses andidentification of tissue type, it is unreasonable to validatequantitative structural dimensions in a specimen by making comparisonsbetween in situ OCT measurements and histology. Other complicationsfrequently arise because histology shrinkage artifacts can occuranisotropically (causing twisting and nonlinear distortion) andregistration between OCT images and histology images is imprecise andqualitative at best. Inasmuch as uncertainty in dimensions extractedfrom an OCT image is due to finite resolution (<5 μm) or uncertainty intissue refractive index (≈5%), the PS-OCT configurations are moreaccurate than histology for in situ dimensional analysis of lamellarthickness or fiber orientation in the annulus fibrosis and other tissuesexhibiting similar geometries. Additionally, a PS-OCT cross sectionprovides the orientation of fibers into and out of the B-scan plane,whereas a histological analysis cannot reveal this three-dimensionalstructure without a complex process of registering multiple sectionstaken parallel to the lamellae at successively deeper locations.

Decreasing polarimetric speckle noise (σ_(speckle)) by ensembleaveraging effectively detects changes in θ(z). Although 90° changes inannulus fibrous fiber orientation (θ) result in dramatic spikes in κ(z),as shown in FIGS. 18A-B, other specimens may exhibit less-dramaticS_(m)(z) trajectory changes which are more difficult to detect withoutadditional σ_(speckle) reduction. Algorithms to automatically detectchanges in S_(m)(z) trajectories will be more robust with adequateσ_(speckle) reduction. Average σ_(speckle) in the specimen was 7° anddid not show appreciable variation with depth (z).

The PS-OCT configuration collects ultrastructural information similar tothat acquired using histology. Polarization-related properties such asfiber orientation (θ(x, z)) can be used to identify and quantifystructural properties (e.g., thickness) in OCT images, regardless ofpoor contrast in the backscattered intensity B-scan image. ComprehensivePS-OCT imaging of cartilage structures may elucidate injury mechanisms,stress distribution and age variables as well as provide feedback onnovel treatment approaches or engineered cartilage-replacementconstructs.

The embodiment described herein are based on aspects which have beendisclosed by the inventors in disclosure, Kim E and Milner T E, J. Opt.Soc. Am. A. 23: 1458-1467 (2006), hereby incorporated by reference,“High-sensitivity Determination of Birefringence in Turbid Media withEnhanced Polarization-sensitive Optical Coherence Tomography” by Nate J.Kemp et al., J. Opt. Soc. Am. A. 22: 552-560 (2005); “Form-biattenuancein Fibrous Tissues Measured with Polarization-sensitive OpticalCoherence Tomography (PS-OCT)” by Nate J. Kemp et al., Optics Express13: 4611-4628, (2005); and “Fiber Orientation Contrast forDepth-resolved Identification of Structural Interfaces in BirefringentTissue” by Nate J. Kemp et al., Phys. Med. Biol. 51: 3759-3767 (2006),all of which are incorporated by reference herein.

Additional objects, advantages and novel features of the embodiments asset forth in the description, will be apparent to one skilled in the artafter reading the foregoing detailed description or may be learned bypractice of the embodiments. The objects and advantages of theembodiments may be realized and attained by means of the instruments andcombinations particularly pointed out here.

1. A spectral interferometer for analyzing a sample comprising: a lightsource that produces light over a multiplicity of optical frequencies;at least one optical fiber through which the light is transmitted to thesample; a receiver which receives the light reflected from the sample;and a computer coupled to the receiver that determines polarizationproperties of the sample.
 2. The interferometer as described in claim 1,further comprising an optical spectrum analyzer coupled to the receiver,wherein the optical spectrum analyzer records the intensity of light atthe output of the interferometer.
 3. The interferometer as described inclaim 2, wherein the computer determines simultaneously the depth andpolarimetric properties of the light reflected from the sample.
 4. Theinterferometer as described in claim 2, wherein the computer determinesvariations of the polarization of the reflected light as a function ofdepth of the sample.
 5. The interferometer as described in claim 2,wherein the computer determines birefringence of the sample,biattenuance of the sample, retardation of the sample, or optical axisof the sample.
 6. The interferometer as described in claim 3, whereinthe computer identifies tissue type of the sample as a function of depthfrom the depth-resolved birefringence, depth resolved biattenuance,depth resolved retardation, or depth resolved optical axis of thesample.
 7. The interferometer as described in claim 3, wherein theoptical fiber is coupled to a catheter.
 8. The interferometer asdescribed in claim 3, wherein the computer identifies the tissue type ofthe sample by the polarization properties as function of depth from thedepth-resolved birefringence of the sample by employing a multi-statenonlinear algorithm that uses M incident polarization states uniformlydistributed on a great circle of the Poincaré sphere and utilizingmultiple incident polarization states to gives M distinctseparation-angles (γ_(m)) distributed within the interval.
 9. Apolarization-sensitive optical coherence tomography apparatuscomprising: a broadband frequency-swept laser source optically coupledto an interferometer; an auxiliary wavemeter optically coupled to theinterferometer; and a detection path optically coupled to a computer todetermine the depth-resolved polarization properties of a sample. 10.The apparatus as described in claim 9, wherein the computersimultaneously determines the depth and polarimetric properties of thelight reflected from the sample.
 11. The apparatus as described in claim10, wherein the computer determines variations of the polarization ofthe reflected light as a function of depth of the sample.
 12. Theapparatus as described in claim 9, wherein the computer determinesbirefringence of the sample, biattenuance of the sample, retardation ofthe sample, optical axis of the sample.
 13. The apparatus as describedin claim 9, wherein the computer identifies the tissue type of thesample as a function of depth from the depth-resolved birefringence,depth-resolved biattenuance, depth-resolved retardation, anddepth-resolved optical axis of the sample.
 14. The apparatus asdescribed in claim 13, wherein the interferometer is coupled to acatheter.
 15. The apparatus as described in claim 9, wherein thecomputer identifies the tissue type of the sample by the polarizationproperties as function of depth from the depth-resolved birefringence ofthe sample by employing a multi-state nonlinear algorithm that uses Mincident polarization states uniformly distributed on a great circle ofthe Poincaré sphere and utilizing multiple incident polarization statesto gives M distinct separation-angles (γ_(m)) distributed within theinterval.
 16. The apparatus as described in claim 1, wherein the sampleincludes a tissue selected from the group consisting of: arterialvessels and plaques, amyloid plaques and neurofibrillary tangles,aneurysms, urethra, tumors, cartilage, cornea, muscle, retina, nerve,skin and tendon.
 17. The apparatus as described in claim 1, wherein thesample includes a disease tissue selected from the group consisting of:osteoarthritis, myocardial heart disease, thyroid disease, aneurism,gout, Alzheimer's disease, cancers, tumors, glaucoma, and chronicmyeloid leukemia.
 18. The apparatus as described in claim 1, wherein thesample includes a tissue subjected to one of the following: burns, woundhealing, optical clearing by exogenous chemical agents, or thecontractile state of muscle.
 19. The apparatus as described in claim 9,wherein the sample includes a tissue selected from the group consistingof: arterial vessels and plaques, amyloid plaques and neurofibrillarytangles, aneurysms, urethra, tumors, cartilage, cornea, muscle, retina,nerve, skin and tendon.
 20. The apparatus as described in claim 9,wherein the sample includes a disease tissue selected from the groupconsisting of: osteoarthritis, myocardial heart disease, thyroiddisease, aneurism, gout, Alzheimer's disease, cancers, tumors, glaucoma,and chronic myeloid leukemia.